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Journal articles on the topic 'Lp space'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Cambern, Michael, Krzysztof Jarosz, and Georg Wodinski. "Almost-Lp-projections and Lp isomorphisms." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 113, no. 1-2 (1989): 13–25. http://dx.doi.org/10.1017/s0308210500023921.

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SynopsisLp -summands and Lp -projections in Banach spaces have been studied by E. Behrends, who showed that for a fixed value of p, l ≦ p ≦ ∞, p ≠ 2, any two Lp -projections on a given Banach space E commute. Here we introduce the notion of almost-Lp -projections, and we establish a result which generalises Behrends' theorem, while also simplifying its proof. Almost-Lp-projections are then applied to the study of small-bound isomorphisms of Bochner LP -spaces. It is shown that if the Banach space E satisfies a geometric condition which, in the finite-dimensional case, reduces to the absence of

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2

Carothers, N. L., and S. J. Dilworth. "Some Banach space embeddings of classical function spaces." Bulletin of the Australian Mathematical Society 43, no. 1 (1991): 73–77. http://dx.doi.org/10.1017/s0004972700028781.

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3

Greim, Peter, James E. Jamison, and Anna Kamińska. "Almost transitivity of some function spaces." Mathematical Proceedings of the Cambridge Philosophical Society 116, no. 3 (1994): 475–88. http://dx.doi.org/10.1017/s0305004100072753.

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AbstractThe almost transitive norm problem is studied for Lp (μ, X), C(K, X) and for certain Orlicz and Musielak-Orlicz spaces. For example if p ≠ 2 < ∞ then Lp (μ) has almost transitive norm if and only if the measure μ is homogeneous. It is shown that the only Musielak-Orlicz space with almost transitive norm is the Lp-space. Furthermore, an Orlicz space has an almost transitive norm if and only if the norm is maximal. Lp (μ, X) has almost transitive norm if Lp(μ) and X have. Separable spaces with non-trivial Lp-structure fail to have transitive norms. Spaces with nontrivial centralizers

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4

De Squire, Maria Torres. "Multipliers from spaces of test functions to amalgams." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 54, no. 1 (1993): 97–110. http://dx.doi.org/10.1017/s1446788700037010.

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AbstractIn this paper we study the space of multipliers M(r, s: p, q) from the space of test functions Φrs(G), on a locally compact abelian group G, to amalgams (Lp, lq)(G); the former includes (when r = s = ∞) the space of continuous functions with compact support and the latter are extensions of the Lp(G) spaces. We prove that the space M(∞: p) is equal to the derived space (Lp)0 defined by Figá-Talamanca and give a characterization of the Fourier transform for amalgams in terms of these spaces of multipliers.

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5

Aydin, İsmail. "On Variable Exponent Amalgam Spaces." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 3 (2012): 5–20. http://dx.doi.org/10.2478/v10309-012-0051-2.

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Abstract We derive some of the basic properties of weighted variable exponent Lebesgue spaces Lp(.)w (ℝn) and investigate embeddings of these spaces under some conditions. Also a new family of Wiener amalgam spaces W(Lp(.)w ;Lqv) is defined, where the local component is a weighted variable exponent Lebesgue space Lp(.)w (ℝn) and the global component is a weighted Lebesgue space Lqv (ℝn) : We investigate the properties of the spaces W(Lp(.)w ;Lqv): We also present new Hölder-type inequalities and embeddings for these spaces.

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6

Yaying, Taja, Bipan Hazarika, and S. A. Mohiuddine. "Domain of Padovan q-difference matrix in sequence spaces lp and l∞." Filomat 36, no. 3 (2022): 905–19. http://dx.doi.org/10.2298/fil2203905y.

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In this study, we construct the difference sequence spaces lp (P?2q) = (lp)P?2q, 1 ? p ? ?, where P = (?rs) is an infinite matrix of Padovan numbers %s defined by ?rs = {?s/?r+5-2 0 ? s ? r, 0 s > r. and ?2q is a q-difference operator of second order. We obtain some inclusion relations, topological properties, Schauder basis and ?-, ?- and ?-duals of the newly defined space. We characterize certain matrix classes from the space lp (P?2q) to any one of the space l1, c0, c or l?. We examine some geometric properties and give certain estimation for von-Neumann Jordan constant and James constan

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7

Ravi, Dr J., S. Dickson, and R. Ranjitha. "Analyzation of Weak Convergence on Lp Space." International Journal of Trend in Scientific Research and Development Volume-2, Issue-1 (2017): 1142–49. http://dx.doi.org/10.31142/ijtsrd7194.

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8

Pathak, Ashish, та Shrish Pandey. "Besov-type spaces for the κ-Hankel wavelet transform on the real line". Concrete Operators 8, № 1 (2021): 114–24. http://dx.doi.org/10.1515/conop-2020-0117.

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Abstract In this paper, we shall introduce functions spaces as subspaces of Lp κ (ℝ) that we call Besov-κ-Hankel spaces and extend the concept of κ-Hankel wavelet transform in Lp κ(ℝ) space. Subsequently we will characterize the Besov-κ-Hankel space by using κ-Hankel wavelet coefficients.

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9

Dorokhov, Alexander, and Michael Karpov. "On the existence of fixed points in completely continuous operators in F -space." Tambov University Reports. Series: Natural and Technical Sciences, no. 125 (2019): 26–32. http://dx.doi.org/10.20310/1810-0198-2019-24-125-26-32.

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This work is dedicated to the development of the theory of fixed points of completely continuous operators. We prove existence of new theorems of fixed points of completely continuous operators in F -space (Frechet space). This class of spaces except Banach includes such important space as a countably normed space and Lp(0 < p < 1), lp(0 < p < 1).

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10

Al Ghafri, Mohammed Said, Yousef Estaremi, and Zhidong Huang. "Orlicz Spaces and Their Hyperbolic Composition Operators." Mathematics 12, no. 18 (2024): 2809. http://dx.doi.org/10.3390/math12182809.

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In this paper, by extending some Lp-norm inequalities to similar inequalities for Orlicz space (LΦ-norm), we provide equivalent conditions for composition operators to have the shadowing property on the Orlicz space LΦ(μ). Additionally, we show that for composition operators on Orlicz spaces, the concepts of generalized hyperbolicity and the shadowing property are equivalent. These results extend similar findings on Lp-spaces to Orlicz spaces.

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11

Watase, Yasushige, Noboru Endou, and Yasunari Shidama. "On Lp Space Formed by Real-Valued Partial Functions." Formalized Mathematics 18, no. 3 (2010): 159–69. http://dx.doi.org/10.2478/v10037-010-0018-6.

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On Lp Space Formed by Real-Valued Partial Functions This article is the continuation of [31]. We define the set of Lp integrable functions - the set of all partial functions whose absolute value raised to the p-th power is integrable. We show that Lp integrable functions form the Lp space. We also prove Minkowski's inequality, Hölder's inequality and that Lp space is Banach space ([15], [27]).

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12

Fidaleo, Francesco. "Canonical Operator Space Structures on Non-Commutative Lp Spaces." Journal of Functional Analysis 169, no. 1 (1999): 226–50. http://dx.doi.org/10.1006/jfan.1999.3498.

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13

Li, Pengtao, та Zhichun Zhai. "Application of Capacities to Space-Time Fractional Dissipative Equations II: Carleson Measure Characterization for Lq(ℝ+n+1,μ) L^q (\mathbb{R}_ + ^{n + 1} ,\mu ) −Extension". Advances in Nonlinear Analysis 11, № 1 (2022): 850–87. http://dx.doi.org/10.1515/anona-2021-0232.

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Abstract This paper provides the Carleson characterization of the extension of fractional Sobolev spaces and Lebesgue spaces to L q ( ℝ + n + 1 , μ ) L^q (\mathbb{R}_ + ^{n + 1} ,\mu ) via space-time fractional equations. For the extension of fractional Sobolev spaces, preliminary results including estimates, involving the fractional capacity, measures, the non-tangential maximal function, and an estimate of the Riesz integral of the space-time fractional heat kernel, are provided. For the extension of Lebesgue spaces, a new Lp –capacity associated to the spatial-time fractional equations is i

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14

Zhao, Junjian, Marko Kostić, and Wei-Shih Du. "On New Decomposition Theorems for Mixed-Norm Besov Spaces with Ingredient Modulus of Smoothness." Symmetry 15, no. 3 (2023): 642. http://dx.doi.org/10.3390/sym15030642.

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In this paper, we introduce and study the concept of the ingredient modulus of smoothness in component form in Lp→(Rd) and a kind of mixed-norm Sobolev space. We obtain some new properties, inequalities, and auxiliary results in mixed-norm spaces Lp→(Rd). In addition, a new concept of mixed-norm Besov space is presented and a new decomposition theorem for mixed-norm Besov spaces is established.

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15

Ragusa, Maria Alessandra, and Veli B. Shakhmurov. "A Navier–Stokes-Type Problem with High-Order Elliptic Operator and Applications." Mathematics 8, no. 12 (2020): 2256. http://dx.doi.org/10.3390/math8122256.

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The existence, uniqueness and uniformly Lp estimates for solutions of a high-order abstract Navier–Stokes problem on half space are derived. The equation involves an abstract operator in a Banach space E and small parameters. Since the Banach space E is arbitrary and A is a possible linear operator, by choosing spaces E and operators A, the existence, uniqueness and Lp estimates of solutions for numerous classes of Navier–Stokes type problems are obtained. In application, the existence, uniqueness and uniformly Lp estimates for the solution of the Wentzell–Robin-type mixed problem for the Navi

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16

Raynaud, Yves. "A note on symmetric basic sequences in Lp(Lq)." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 1 (1992): 183–94. http://dx.doi.org/10.1017/s0305004100070869.

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Subspaces of Lp spanned by symmetric independent identically distributed random variables were identified as Orlicz spaces by Bretagnolle and Dacunha-Castelle[1], who showed that, conversely, in the case p ≤ 2, every p-convex, 2-concave Orlicz space is isomorphic to a subspace of Lp. This was extended by Dacunha-Castelle [3] to subspaces of Lp with symmetric basis, which appear as ‘p-means’ of Orlicz spaces (see [9] for the corresponding finite-dimensional result, and [12] for the case of rearrangement invariant function spaces). On the contrary the only subspaces with symmetric basis of Lp fo

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17

Nasir, Muhammad, Fehaid Salem Alshammari, and Ali Raza. "Bessel–Riesz Operator in Variable Lebesgue Spaces Lp(·)(R+)." Axioms 14, no. 6 (2025): 429. https://doi.org/10.3390/axioms14060429.

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This paper investigates the Bessel–Riesz operator within the framework of variable Lebesgue spaces. We extend existing results by establishing boundedness under more general conditions. The analysis is based on the Hardy–Littlewood maximal function, Hölder’s inequality, and dyadic decomposition techniques. For a given domain space, we construct a suitable range space such that the operator remains bounded. Conversely, for a prescribed range space, we identify a corresponding domain space that guarantees boundedness. Illustrative examples are included to demonstrate the construction of such spa

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18

COWLING, MICHAEL G., and MICHAEL LEINERT. "POINTWISE CONVERGENCE AND SEMIGROUPS ACTING ON VECTOR-VALUED FUNCTIONS." Bulletin of the Australian Mathematical Society 84, no. 1 (2011): 44–48. http://dx.doi.org/10.1017/s0004972710002030.

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AbstractA submarkovian C0 semigroup (Tt)t∈ℝ+ acting on the scale of complex-valued functions Lp(X,ℂ) extends to a semigroup of operators on the scale of vector-valued function spaces Lp(X,E), when E is a Banach space. It is known that, if f∈Lp(X,ℂ), where 1<p<∞, then Ttf→f pointwise almost everywhere. We show that the same holds when f∈Lp(X,E) .

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19

Riečan, Beloslav. "On the LP space of observables." Fuzzy Sets and Systems 105, no. 2 (1999): 299–306. http://dx.doi.org/10.1016/s0165-0114(98)00329-7.

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20

Pichugov, S. A. "Jung's constant for the space Lp." Mathematical Notes of the Academy of Sciences of the USSR 43, no. 5 (1988): 348–54. http://dx.doi.org/10.1007/bf01158839.

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21

Borwein, P. B., T. F. Xie, and S. P. Zhou. "On approximation by trigonometric Lagrange interpolating polynomials II." Bulletin of the Australian Mathematical Society 45, no. 2 (1992): 215–21. http://dx.doi.org/10.1017/s0004972700030070.

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We show that trigonometric Lagrange interpolating approximation with arbitrary real distinct nodes in Lp space for 1 ≤ p < ∞, as that with equally spaced nodes in Lp space for 1 < p < ∞ in an earlier paper by T.F. Xie and S.P. Zhou, may also be arbitrarily “bad”. This paper is a continuation of this earlier work by Xie and Zhou, but uses a different method.

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22

Sarantopoulos, I. "Estimates for polynomial norms on Lp(μ) spaces". Mathematical Proceedings of the Cambridge Philosophical Society 99, № 2 (1986): 263–71. http://dx.doi.org/10.1017/s0305004100064185.

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AbstractIf L is a symmetric m-linear form on a Banach space and L^ is the associated polynomial thenFor special choices of Banach space this inequality can be improved. This has been done by Harris [5] in the case of the Lp(μ) spaces. In this paper we improve his estimates and disprove one of his conjectures.

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23

Xu, Quanhua. "A description of (Cp[Lp(M)], Rp[Lp(M)])θ". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135, № 5 (2005): 1073–84. http://dx.doi.org/10.1017/s0308210500004273.

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24

Xu, Quanhua. "A description of (Cp[Lp(M)], Rp[Lp(M)])θ". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135, № 5 (2005): 1073–84. http://dx.doi.org/10.1017/s0308210505000557.

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25

CHILIN, V. I., and B. A. RAKHIMOV. "CRITERIA OF COMPACTNESS IN Lp - SPACES." International Journal of Modern Physics: Conference Series 09 (January 2012): 520–28. http://dx.doi.org/10.1142/s2010194512005612.

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The problems of mathematical biology, as a rule, are formulated in terms of independent and depended (unknown) variables (functions), and operators (mostly differential operators). These variables belong to some spaces and operators acting in these spaces. Both, unknown variables and operators, follow the main rules of these spaces as metrics, topology and etc. In applications a solution of the problem will be constructed by approximation methods based on metrics/topology of the space. In this convergence of the constructed approximations essentially depends on compactness.

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26

Yii Sern Christopher Heng, Farhana Mohd Razif, Sharifah Fairuz Syed Fadzil, Louis Ting Kwang Liou, and Boon Jia Jun. "Daylighting Performance of Integrated Venetian Blinds with Horizontal Light Pipe System for Deep Plan High-Rise Office in Tropical Climate." Journal of Advanced Research in Applied Sciences and Engineering Technology 28, no. 3 (2022): 144–53. http://dx.doi.org/10.37934/araset.28.3.144153.

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A substantial amount of daylight is received by tropical countries like Malaysia. There are advantages and disadvantages to using this renewable resource in a high-rise office building. Such buildings' deep plan spaces make it difficult to create a uniform daylight distribution across the space. A solution for this issue is the usage of an integrated Venetian blind (VB) with a horizontal light pipe (LP). Using an overcast and intermediate sky in South orientation, seven (7) distinct types of VB angle configurations were simulated using the Integrated Environment Solution Virtual Environment (I

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27

Zhang, Houkun, and Jiang Zhou. "Mixed-Norm Amalgam Spaces and Their Predual." Symmetry 14, no. 1 (2022): 74. http://dx.doi.org/10.3390/sym14010074.

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In this paper, we introduce mixed-norm amalgam spaces (Lp→,Ls→)α(Rn) and prove the boundedness of maximal function. Then, the dilation argument obtains the necessary and sufficient conditions of fractional integral operators’ boundedness. Furthermore, the strong estimates of linear commutators [b,Iγ] generated by b∈BMO(Rn) and Iγ on mixed-norm amalgam spaces (Lp→,Ls→)α(Rn) are established as well. In order to obtain the necessary conditions of fractional integral commutators’ boundedness, we introduce mixed-norm Wiener amalgam spaces (Lp→,Ls→)(Rn). We obtain the necessary and sufficient condit

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Al-Saphory, Raheam A. Mansor, and Mahmood K. Jasim. "Quasi-Compactness in Quasi-Banach Spaces." JOURNAL OF ADVANCES IN MATHEMATICS 4, no. 1 (2013): 325–41. http://dx.doi.org/10.24297/jam.v4i1.7227.

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Quasi-compactness in a quasi-Banach space for the sequence space Lp, p< 0 < p <1 has been introduced based on the important extension of Milman's reverse Brunn-Minkowiski inequality by Bastero et al. in 1995. Moreover, Many interesting results connected with quasi-compactness and quasi-completeness in a quasi-normed space, Lp for 0 < p < 1 have been explored. Furthermore, we have shown that, the quasi-normed space under which condition is a quasi Banach space. Also, we have shown that the space if it is quasi-compact in quasi normed space then it is quasi Banach space and the co

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29

P, Govindaraju, Sasikala V, and Mohamed Ali A. "A study on stochastic maximal regularity for rough time-dependent problems." Journal of Computational Mathematica 5, no. 1 (2021): 60–69. http://dx.doi.org/10.26524/cm92.

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We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only progressively measurable in the time variable. For 2m-th order systems with VMO regularity in space, we obtain Lp(Lq) estimates for all p > 2 and q ≥ 2, leading to optimal space-time regularity results. For second order systems with continuous coefficients in space, we also include a first order linear term, under a stochastic parabolicity condition, and obtain L

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30

Bloom, Steven, and Ron Kerman. "Extrapolation of Lp Data from a Modular Inequality." Canadian Mathematical Bulletin 45, no. 1 (2002): 25–35. http://dx.doi.org/10.4153/cmb-2002-003-x.

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AbstractIf an operator T satisfies a modular inequality on a rearrangement invariant space Lρ(Ω, μ), and if p is strictly between the indices of the space, then the Lebesgue inequality holds. This extrapolation result is a partial converse to the usual interpolation results. A modular inequality for Orlicz spaces takes the form , and here, one can extrapolate to the (finite) indices i(Φ) and I(Φ) aswell.

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31

Henson, C. Ward, Yves Raynaud, and Andrew Rizzo. "On Axiomatizability of Non-Commutative Lp-Spaces." Canadian Mathematical Bulletin 50, no. 4 (2007): 519–34. http://dx.doi.org/10.4153/cmb-2007-051-7.

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AbstractIt is shown that Schatten p-classes of operators between Hilbert spaces of different (infinite) dimensions have ultrapowers which are (completely) isometric to non-commutative Lp-spaces. On the other hand, these Schatten classes are not themselves isomorphic to non-commutative Lp spaces. As a consequence, the class of non-commutative Lp-spaces is not axiomatizable in the first-order language developed by Henson and Iovino for normed space structures, neither in the signature of Banach spaces, nor in that of operator spaces. Other examples of the same phenomenon are presented that belon

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32

Hare, Kathryn E., and Enji Sato. "Spaces of Lorentz Multipliers." Canadian Journal of Mathematics 53, no. 3 (2001): 565–91. http://dx.doi.org/10.4153/cjm-2001-024-5.

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AbstractWe study when the spaces of Lorentz multipliers from Lp,t → Lp,s are distinct. Our main interest is the case when s < t, the Lorentz-improving multipliers. We prove, for example, that the space of multipliers which map Lp,t → Lp,s is different from those mapping Lp,t → Lp,s if either r = p or p′ and 1/s − 1/t ≠ 1/u − 1/v, or r ≠ p or p′. These results are obtained by making careful estimates of the Lorentz multiplier norms of certain linear combinations of Fejer or Dirichlet kernels. For the case when the first indices are different the linear combination we analyze is in the spirit

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33

WEHRHEIM, KATRIN. "BANACH SPACE VALUED CAUCHY–RIEMANN EQUATIONS WITH TOTALLY REAL BOUNDARY CONDITIONS." Communications in Contemporary Mathematics 06, no. 04 (2004): 601–35. http://dx.doi.org/10.1142/s0219199704001410.

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The main purpose of this paper is to give a general regularity result for Cauchy–Riemann equations in complex Banach spaces with totally real boundary conditions. The usual elliptic Lp-regularity results hold true under one crucial assumption: The Banach space is isomorphic to a closed subspace of an Lp-space. (Equivalently, the totally real submanifold is modelled on a closed subspace of an Lp-space.) Secondly, we describe a class of examples of such totally real submanifolds, namely gauge invariant Lagrangian submanifolds in the space of connections over a Riemann surface. These pose natural

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34

Castillo, René Erlín, Héctor Chaparro, and Oscar Alejandro Chaparro. "Multiplication operator on weighted Lebesgue sequence spaces." Gulf Journal of Mathematics 19, no. 2 (2025): 77–92. https://doi.org/10.56947/gjom.v19i2.2692.

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In this paper, we study the multiplication operator acting on the Lebesgue sequence space lp, w, for 1 ≤ p ≤ ∞, which generalizes the classical lp spaces by incorporating a weight sequence wn. We focus on properties such as continuity, inverse continuity, finite range, compactness, and essential norm of the operator.

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Hu, Zhibao, and Bor-Luh Lin. "Asymptotic-norming and Mazur intersection properties in Bochner function spaces." Bulletin of the Australian Mathematical Society 48, no. 2 (1993): 177–86. http://dx.doi.org/10.1017/s0004972700015628.

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A Banach space X has the asymptotic-norming property if and only if the Lebesgue-Bochner function space Lp (μ, X) has the asumptotic-norming property for p with 1 < p < ∞. It follows that a Banach space X is Hahn-Banach smooth if and only if Lp (μ, X) is Hahn-Banach smooth for p with 1 < p < ∞. We also show that for p with 1 < p < ∞, (1) if X has the compact Mazur intersection property then so does Lp(μ, X); (2) if the measure μ is not purely atomic, then the space Lp(μ, X) has the Mazur intersection property if and only if X is an Asplund space and has the Mazur intersection

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36

Koldobsky, Alexander. "Isometric Stability Property of Certain Banach Spaces." Canadian Mathematical Bulletin 38, no. 1 (1995): 93–97. http://dx.doi.org/10.4153/cmb-1995-012-9.

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AbstractLet E be one of the spaces C(K) and L1, F be an arbitrary Banach space, p > 1, and (X, σ) be a space with a finite measure. We prove that E is isometric to a subspace of the Lebesgue-Bochner space LP(X; F) only if E is isometric to a subspace of F. Moreover, every isometry T from E into Lp(X; F) has the form Te(x) = h(x)U(x)e, e ∊ E, where h: X —> R is a measurable function and, for every x ∊ X, U(x) is an isometry from E to F

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37

Xie, T. F., and S. P. Zhou. "On approximation by trigonometric Lagrange interpolating polynomials." Bulletin of the Australian Mathematical Society 40, no. 3 (1989): 425–28. http://dx.doi.org/10.1017/s0004972700017482.

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It is well-known that the approximation to f(x) ∈ C2π, by nth trigonometric Lagrange interpolating polynomials with equally spaced nodes in C2π, has an upper bound In(n)En(f), where En(f) is the nth best approximation of f(x). For various natural reasons, one can ask what might happen in Lp space? The present paper indicates that the result about the trigonometric Lagrange interoplating approximation in Lp space for 1 < p < ∞ may be “bad” to an arbitrary degree.

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38

Das, Namita. "Schatten Class Toeplitz Operators on the Bergman Space." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–16. http://dx.doi.org/10.1155/2009/921324.

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We have shown that if the Toeplitz operatorTϕon the Bergman spaceLa2(&#x1D53B;)belongs to the Schatten classSp,1≤p<∞, thenϕ˜∈Lp(&#x1D53B;,dλ), whereϕ˜is the Berezin transform ofϕ,dλ(z)=dA(z)/(1−|z|2)2, anddA(z)is the normalized area measure on the open unit disk&#x1D53B;. Further, ifϕ∈Lp(&#x1D53B;,dλ)thenϕ˜∈Lp(&#x1D53B;,dλ)andTϕ∈Sp. For certain subclasses ofL∞(&#x1D53B;), necessary and sufficient conditions characterizing Schatten class Toeplitz operators are also obtained.

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39

Zhang, Qinghua, Yueping Zhu, and Feng Wang. "Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces." Journal of Function Spaces 2020 (March 10, 2020): 1–9. http://dx.doi.org/10.1155/2020/3672892.

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This paper is devoted to the maximal regularity of sectorial operators in Lebesgue spaces Lp⋅ with a variable exponent. By extending the boundedness of singular integral operators in variable Lebesgue spaces from scalar type to abstract-valued type, the maximal Lp⋅−regularity of sectorial operators is established. This paper also investigates the trace of the maximal regularity space E01,p⋅I, together with the imbedding property of E01,p⋅I into the range-varying function space C−I,X1−1/p⋅,p⋅. Finally, a type of semilinear evolution equations with domain-varying nonlinearities is taken into acc

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Grząślewicz, Ryszard. "Extreme Positive Contractions on Finite Dimensional lp-Spaces." Canadian Journal of Mathematics 37, no. 4 (1985): 682–99. http://dx.doi.org/10.4153/cjm-1985-036-4.

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In this paper we give a characterization of the extreme positive contractions on finite dimensional lp-spaces for 1 < p < ∞. This is related to the characterization of the extreme doubly stochastic operators. In Section 2 we present the basic properties of the facial structure of the set of doubly stochastic n × m matrices. In Section 3 we use these facts for description of the facial structure of the set of positive contractions on finite dimensional lp-space. Next is considered stability of the positive part of the unit ball of operators (Section 5). In Section 7 we prove that extreme

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41

Fleming, R. J., and J. E. Jamison. "Hermitian operators and isometries on sums of Banach spaces." Proceedings of the Edinburgh Mathematical Society 32, no. 2 (1989): 169–91. http://dx.doi.org/10.1017/s0013091500028583.

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Let E be a Banach sequence space with the property that if (αi) ∈ E and |βi|≦|αi| for all i then (βi) ∈ E and ‖(βi)‖E≦‖(αi)‖E. For example E could be co, lp or some Orlicz sequence space. If (Xn) is a sequence of real or complex Banach spaces, then E can be used to construct a vector sequence space which we will call the E sum of the Xn's and symbolize by ⊕EXn. Specifically, ⊕EXn = {(xn)|(xn)∈Xn and (‖xn‖)∈E}. The E sum is a Banach space with norm defined by: ‖(xn)‖ = ‖(‖xn‖)‖E. This type of space has long been the source of examples and counter-examples in the geometric theory of Banach space

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42

Chou, Yu-Lin. "Embedding topological manifolds into Lp spaces." Acta Universitatis Sapientiae, Mathematica 16, no. 1 (2025): 98–100. https://doi.org/10.47745/ausm-2024-0008.

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With a simple argument, we show as a main note that, for every given 1 ≤ p ≤ +∞, every locally compact second-countable Hausdorff space is topologically embeddable into some L p space with respect to some finite nonzero Borel measure, where the embedding may be chosen so that its range is included in some open proper subset of the Lp space.

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43

Asmar, N. H., B. P. Kelly, and S. Montgomery-Smith. "A note on UMD spaces and transference in vector-valued function spaces." Proceedings of the Edinburgh Mathematical Society 39, no. 3 (1996): 485–90. http://dx.doi.org/10.1017/s0013091500023245.

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A Banach space X is called an HT space if the Hilbert transform is bounded from Lp(X) into Lp(X), where 1 < p < ∞. We introduce the notion of an ACF Banach space, that is, a Banach space X for which we have an abstract M. Riesz Theorem for conjugate functions in Lp(X), 1 < p < ∞. Berkson, Gillespie and Muhly [5] showed that X ∈ HT ⇒ X ∈ ACF. In this note, we will show that X ∈ ACF ⇒ X ∈ UMD, thus providing a new proof of Bourgain's result X ∈ HT ⇒ X ∈ UMD.

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44

Pichugov, S. A. "Jung's relative constant of the space Lp." Ukrainian Mathematical Journal 42, no. 1 (1990): 111–13. http://dx.doi.org/10.1007/bf01066372.

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Metafune, G., and V. B. Moscatelli. "On the Space lp+ = ∩lqq>p." Mathematische Nachrichten 147, no. 1 (1990): 7–12. http://dx.doi.org/10.1002/mana.19901470102.

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JI, LIZHEN, and ANDREAS WEBER. "Dynamics of the heat semigroup on symmetric spaces." Ergodic Theory and Dynamical Systems 30, no. 2 (2009): 457–68. http://dx.doi.org/10.1017/s0143385709000133.

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AbstractThe aim of this paper is to show that the dynamics of Lp heat semigroups (p>2) on a symmetric space of non-compact type is very different from the dynamics of the Lp heat semigroups if 1<p≤2. To see this, we show that certain shifts of the Lp heat semigroups have a chaotic behavior if p>2, and that such a behavior is not possible in the cases 1<p≤2. These results are compared with the corresponding situation for Euclidean spaces and symmetric spaces of compact type, where such a behavior is not possible.

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Aykol, Canay, and Esra Kaya. "B−maximal operators, B−singular integral operators and B−Riesz potentials in variable exponent Lorentz spaces." Filomat 37, no. 17 (2023): 5765–74. http://dx.doi.org/10.2298/fil2317765a.

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In this paper, we prove the boundedness of B?maximal operator, B?singular integral operator and B?Riesz potential in the variable exponent Lorentz space Lp(?),q(?),?(Rn k,+). As a consequence of the boundedness of B?Riesz potentials in variable exponent Lorentz spaces, we also obtain that B?fractional maximal operators are bounded in Lp(?),q(?),?(Rn k,+).

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Zlatanov, B. "Schur property and lP isomorphic copies in Musielak–Orlicz sequence spaces." Bulletin of the Australian Mathematical Society 75, no. 2 (2007): 193–210. http://dx.doi.org/10.1017/s0004972700039137.

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The author shows that if the dual of a Musielak–Orlicz sequence space lΦ is a stabilized asymptotic l∞, space with respect to the unit vector basis, then lΦ is saturated with complemented copies of l1 and has the Schur property. A sufficient condition is found for the isomorphic embedding of lp spaces into Musielak–Orlicz sequence spaces.

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Carmichael, Richard D. "Generalized Vector-Valued Hardy Functions." Axioms 11, no. 2 (2022): 39. http://dx.doi.org/10.3390/axioms11020039.

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We consider analytic functions in tubes Rn+iB⊂Cn with values in Banach space or Hilbert space. The base of the tube B will be a proper open connected subset of Rn, an open connected cone in Rn, an open convex cone in Rn, and a regular cone in Rn, with this latter cone being an open convex cone which does not contain any entire straight lines. The analytic functions satisfy several different growth conditions in Lp norm, and all of the resulting spaces of analytic functions generalize the vector valued Hardy space Hp in Cn. The analytic functions are represented as the Fourier–Laplace transform

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Gunawan, Hendra. "The space of p-summable sequences and its natural n-norm." Bulletin of the Australian Mathematical Society 64, no. 1 (2001): 137–47. http://dx.doi.org/10.1017/s0004972700019754.

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We study the space lp, 1 ≤ p ≤ ∞, and its natural n-norm, which can viewed as a generalisation of its usual norm. Using a derived norm equivalent to its usual norm, we show that lp is complete with respect to its natural n-norm. In addition, we also prove a fixed point theorem for lp as an n-normed space.

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