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Journal articles on the topic 'Bloch space'

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Published: 4 June 2021
Last updated: 15 February 2022

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1

Xiao, Zhijing. "WEIGHTED BERGMAN SPACES, BLOCH SPACE AND DING SPACE." Acta Mathematica Scientia 9, no. 3 (September 1989): 265–76. http://dx.doi.org/10.1016/s0252-9602(18)30352-7.

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2

Tjani, Maria. "Distance of a Bloch Function to the Little Bloch Space." Bulletin of the Australian Mathematical Society 74, no. 1 (January 2006): 101–19. http://dx.doi.org/10.1017/s0004972700047493.

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Motivated by a formula of P. Jones that gives the distance of a Bloch function to BMOA, the space of bounded mean oscillations, we obtain several formulas for the distance of a Bloch function to the little Bloch space, β0. Immediate consequences are equivalent expressions for functions in β0. We also give several examples of distances of specific functions to β0. We comment on connections between distance to β0 and the essential norm of some composition operators on the Bloch space, β. Finally we show that the distance formulas in β have Bloch type spaces analogues.
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3

Stroethoff, Karel. "Nevanlinna-type characterizations for the Bloch space and related spaces." Proceedings of the Edinburgh Mathematical Society 33, no. 1 (February 1990): 123–41. http://dx.doi.org/10.1017/s0013091500028947.

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We give a characterisation of the Bloch space in terms of an area version of the Nevanlinna characteristic, analogous to Baernstein's description of the space BMOA in terms of the usual Nevanlinna characteristic. We prove analogous results for the little Bloch space and the space VMOA, and give value distribution characterizations for all these spaces. Finally we give valence conditions on a Bloch or little Bloch function for containment in BMOA or VMOA.
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4

Stroethoff, Karel. "Besov-type characterisations for the Bloch space." Bulletin of the Australian Mathematical Society 39, no. 3 (June 1989): 405–20. http://dx.doi.org/10.1017/s0004972700003324.

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We will prove local and global Besov-type characterisations for the Bloch space and the little Bloch space. As a special case we obtain that the Bloch space consists of those analytic functions on the unit disc whose restrictions to pseudo-hyperbolic discs (of fixed pseudo-hyperbolic radius) uniformly belong to the Besov space. We also generalise the results to Bloch functions and little Bloch functions on the unit ball in . Finally we discuss the related spaces BMOA and VMOA.
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5

Stroethoff, Karel. "The Bloch space and Besov spaces of analytic functions." Bulletin of the Australian Mathematical Society 54, no. 2 (October 1996): 211–19. http://dx.doi.org/10.1017/s0004972700017676.

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We shall give an elementary proof of a characterisation for the Bloch space due to Holland and Walsh, and obtain analogous characterisations for the little Bloch space and Besov spaces of analytic functions on the unit disk in the complex plane.
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6

Cheng, Yuan, Sanjay Kumar, and Ze Hua Zhou. "Composition operators on Dirichlet spaces and Bloch space." Acta Mathematica Sinica, English Series 30, no. 10 (September 5, 2014): 1775–84. http://dx.doi.org/10.1007/s10114-014-3171-y.

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7

Galanopoulos, Petros, Nacho Monreal Galán, and Jordi Pau. "Closure of Hardy spaces in the Bloch space." Journal of Mathematical Analysis and Applications 429, no. 2 (September 2015): 1214–21. http://dx.doi.org/10.1016/j.jmaa.2015.04.075.

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8

ARENDT, W., I. CHALENDAR, M. KUMAR, and S. SRIVASTAVA. "POWERS OF COMPOSITION OPERATORS: ASYMPTOTIC BEHAVIOUR ON BERGMAN, DIRICHLET AND BLOCH SPACES." Journal of the Australian Mathematical Society 108, no. 3 (November 27, 2019): 289–320. http://dx.doi.org/10.1017/s1446788719000235.

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We study the asymptotic behaviour of the powers of a composition operator on various Banach spaces of holomorphic functions on the disc, namely, standard weighted Bergman spaces (finite and infinite order), Bloch space, little Bloch space, Bloch-type space and Dirichlet space. Moreover, we give a complete characterization of those composition operators that are similar to an isometry on these various Banach spaces. We conclude by studying the asymptotic behaviour of semigroups of composition operators on these various Banach spaces.
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9

Hu, Nanhui, and Xiangling Zhu. "Composition Operators and the Closure of Morrey Space in the Bloch Space." Journal of Function Spaces 2019 (April 1, 2019): 1–6. http://dx.doi.org/10.1155/2019/2834865.

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In this paper, we characterize the closure of the Morrey space in the Bloch space. Furthermore, the boundedness and compactness of composition operators from the Bloch space to the closure of the Morrey space in the Bloch space are investigated.
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10

Lindstróm, Mikael, Shamil Makhmutov, and Jari Taskinen. "The Essential Norm of a Bloch-to-Qp Composition Operator." Canadian Mathematical Bulletin 47, no. 1 (March 1, 2004): 49–59. http://dx.doi.org/10.4153/cmb-2004-007-6.

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AbstractThe Qp spaces coincide with the Bloch space for p > 1 and are subspaces of BMOA for 0 < p ≤ 1. We obtain lower and upper estimates for the essential norm of a composition operator from the Bloch space into Qp, in particular from the Bloch space into BMOA.
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11

Jevtic, Miroljub, and Miroslav Pavlovic. "On M-Harmonic Bloch Space." Proceedings of the American Mathematical Society 123, no. 5 (May 1995): 1385. http://dx.doi.org/10.2307/2161125.

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12

Churchill, J. N., and F. E. Holmstrom. "Bloch oscillations in free space?" Physics Letters A 143, no. 1-2 (January 1990): 20–24. http://dx.doi.org/10.1016/0375-9601(90)90791-l.

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13

ZHOU, Zehua. "Composition operators between p-Bloch space and q-Bloch space in the unit ball." Progress in Natural Science 13, no. 3 (2003): 233. http://dx.doi.org/10.1360/03jz9041.

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14

Zhou, Zehua, and Honggang Zeng. "Composition operators between p -Bloch space and q -Bloch space in the unit ball*." Progress in Natural Science 13, no. 3 (March 1, 2003): 233–36. http://dx.doi.org/10.1080/10020070312331343450.

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15

Songxiao, Li, and Zhu Xiangling. "Essential norm of weighted composition operator betweenα-Bloch space andβ-Bloch space in polydiscs." International Journal of Mathematics and Mathematical Sciences 2004, no. 71 (2004): 3941–50. http://dx.doi.org/10.1155/s0161171204403548.

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Letφ(z)=(φ1(z),…,φn(z))be a holomorphic self-map of&#x1D53B;nandψ(z)a holomorphic function on&#x1D53B;n, where&#x1D53B;nis the unit polydiscs ofℂn. Let0<α,β<1, we compute the essential norm of a weighted composition operatorψCφbetweenα-Bloch spaceℬα(&#x1D53B;n)andβ-Bloch spaceℬβ(&#x1D53B;n).
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16

Hu, Qinghua, and Songxiao Li. "Essential norm of weighted composition operators from the Bloch space and the Zygmund space to the Bloch space." Filomat 32, no. 2 (2018): 681–91. http://dx.doi.org/10.2298/fil1802681h.

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17

Kwon, E. G. "A characterization of Bloch space and Besov space." Journal of Mathematical Analysis and Applications 324, no. 2 (December 2006): 1429–37. http://dx.doi.org/10.1016/j.jmaa.2006.01.052.

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18

Galanopoulos, Petros, and Daniel Girela. "The closure of Dirichlet spaces in the Bloch space." Annales Academiae Scientiarum Fennicae Mathematica 44, no. 1 (February 2019): 91–101. http://dx.doi.org/10.5186/aasfm.2019.4402.

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19

Zhu, Kehe. "The Bergman Spaces, The Bloch Space, and Gleason's Problem." Transactions of the American Mathematical Society 309, no. 1 (September 1988): 253. http://dx.doi.org/10.2307/2001168.

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20

Li, Songxiao, and Stevo Stević. "Riemann–Stieltjes operators fromH∞space to α-Bloch spaces." Integral Transforms and Special Functions 19, no. 11 (November 2008): 767–76. http://dx.doi.org/10.1080/10652460701510543.

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21

Zhu, Ke He. "The Bergman spaces, the Bloch space, and Gleason’s problem." Transactions of the American Mathematical Society 309, no. 1 (January 1, 1988): 253. http://dx.doi.org/10.1090/s0002-9947-1988-0931533-6.

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22

YONEDA, Rikio. "Characterizations of Bloch space and Besov spaces by oscillations." Hokkaido Mathematical Journal 29, no. 2 (February 2000): 409–51. http://dx.doi.org/10.14492/hokmj/1350912980.

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23

Choe, Boo Rim. "Projections, the weighted Bergman spaces, and the Bloch space." Proceedings of the American Mathematical Society 108, no. 1 (January 1, 1990): 127. http://dx.doi.org/10.1090/s0002-9939-1990-0991692-0.

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24

Álvarez, Venancio, M. Auxiliadora Márquez, and Dragan Vukotić. "Superposition operators between the Bloch space and Bergman spaces." Arkiv för Matematik 42, no. 2 (October 2004): 205–16. http://dx.doi.org/10.1007/bf02385476.

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25

Aulaskari, Rauno, and Ruhan Zhao. "Composition operators and closures of some Möbius invariant spaces in the Bloch space." MATHEMATICA SCANDINAVICA 107, no. 1 (September 1, 2010): 139. http://dx.doi.org/10.7146/math.scand.a-15147.

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26

Castillo, René E., Julio C. Ramos-Fernández, and Edixon M. Rojas. "A New Essential Norm Estimate of Composition Operators from Weighted Bloch Space into -Bloch Spaces." Journal of Function Spaces and Applications 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/817278.

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Let be any weight function defined on the unit disk and let be an analytic self-map of . In the present paper, we show that the essential norm of composition operator mapping from the weighted Bloch space to -Bloch space is comparable to where for , is a certain special function in the weighted Bloch space. As a consequence of our estimate, we extend the results about the compactness of composition operators due to Tjani (2003).
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27

Zhao, Ruhan. "Hankel operators from the space of bounded analytic functions to the Bloch space." Bulletin of the Australian Mathematical Society 59, no. 1 (February 1999): 53–58. http://dx.doi.org/10.1017/s0004972700032597.

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28

Ohno, Shûichi, and Ruhan Zhao. "Weighted composition operators on the Bloch space." Bulletin of the Australian Mathematical Society 63, no. 2 (April 2001): 177–85. http://dx.doi.org/10.1017/s0004972700019250.

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We characterise bounded and compact weighted composition operators on the Bloch space and the little Bloch space. The results generalise the known corresponding results on composition operators and pointwise multipliers on the Bloch space and the little Bloch space.
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29

Zhou, Hang, and Ze-Hua Zhou. "Weighted Differentiation Composition Operators from the α-Bloch Space to the $\alpha-$Bloch-Orlicz Space." Operators and Matrices, no. 2 (2019): 477–87. http://dx.doi.org/10.7153/oam-2019-13-36.

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30

Li, Songxiao, and Jizhen Zhou. "Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space." AIMS Mathematics 6, no. 4 (2021): 3305–18. http://dx.doi.org/10.3934/math.2021198.

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31

RAMOS-FERNÁNDEZ, JULIO C. "A NEW ESSENTIAL NORM ESTIMATE OF COMPOSITION OPERATORS FROM α-BLOCH SPACES INTO μ-BLOCH SPACES." International Journal of Mathematics 24, no. 14 (December 2013): 1350104. http://dx.doi.org/10.1142/s0129167x13501048.

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Let μ be any weight function defined on the unit disk 𝔻 and let ϕ be an analytic self-map of 𝔻. In this paper, we show that the essential norm of composition operator Cϕ mapping from the α-Bloch space, with α > 0, to μ-Bloch space [Formula: see text] is comparable to [Formula: see text] where, for a ∈ 𝔻, σa is a certain special function in α-Bloch space. As a consequence of our estimate, we extend recent results, about the compactness of composition operators, due to Tjani in [Compact composition operators on Besov spaces, Trans. Amer. Math. Soc.355(11) (2003) 4683–4698] and Malavé Ramírez and Ramos-Fernández in [On a criterion for continuity and compactness of composition operators acting on α-Bloch spaces, C. R. Math. Acad. Sci. Paris351 (2013) 23–26, http://dx.doi.org/10.1016/j.crma.2012.11.013 ].
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32

Zhang, Yanhua. "Toeplitz Operator and Carleson Measure on Weighted Bloch Spaces." Journal of Function Spaces 2019 (February 17, 2019): 1–5. http://dx.doi.org/10.1155/2019/4358959.

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33

Lou, Zengjian. "Composition operators on Qp spaces." Journal of the Australian Mathematical Society 70, no. 2 (April 2001): 161–88. http://dx.doi.org/10.1017/s1446788700002585.

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AbstractA holomorphic map ψ of the unit disk ito itself induces an operator Cψ on holomorphic functions by composition. We characterize bounded and compact composition operators Cψ on Qp spaces, which coincide with the BMOA for p = 1 and Bloch spaces for p > 1. We also give boundedness and compactness characterizations of Cψ from analytic function space X to Qp spaces, X = Dirichlet space D, Bloch space B or B0 = {f: f′ ∈ H∞}.
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34

Reséndis O., L. F., and L. M. Tovar S. "Bicomplex Bergman and Bloch spaces." Arabian Journal of Mathematics 9, no. 3 (July 1, 2020): 665–79. http://dx.doi.org/10.1007/s40065-020-00285-y.

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Abstract In this article, we define the bicomplex weighted Bergman spaces on the bidisk and their associated weighted Bergman projections, where the respective Bergman kernels are determined. We study also the bicomplex Bergman projection onto the bicomplex Bloch space.
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35

Li, Songxiao. "On an integral-type operator from the Bloch space into the QK(p,q) space." Filomat 26, no. 2 (2012): 331–39. http://dx.doi.org/10.2298/fil1202331l.

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Let n be a positive integer, 1 ? H(D) and ? be an analytic self-map of D. The boundedness and compactness of the integral operator (Cn ?,1 f )(z) = ?z 0 f (n)(?(?))1(?)d? from the Bloch and little Bloch space into the spaces QK(p, q) and QK,0(p, q) are characterized.
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36

Pavlovic, Miroslav. "Logarithmic Bloch space and its predual." Publications de l'Institut Math?matique (Belgrade) 100, no. 114 (2016): 1–16. http://dx.doi.org/10.2298/pim1614001p.

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We consider the space B1log?, of analytic functions on the unit disk D, defined by the requirement ?D|f?(z)|?(|z|) dA(z) < ?, where ?(r) = log?(1/(1?r)) and show that it is a predual of the ?log?-Bloch? space and the dual of the corresponding little Bloch space. We prove that a function f(z)=??n=0 an zn with an ? 0 is in B1 log? iff ??n=0 log?(n+2)/(n+1) < ? and apply this to obtain a criterion for membership of the Libera transform of a function with positive coefficients in B1 log?. Some properties of the Cesaro and the Libera operator are considered as well.
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37

Jevti{ć, Miroljub, and Miroslav Pavlovi{ć. "On $\mathcal{M}$-harmonic Bloch space." Proceedings of the American Mathematical Society 123, no. 5 (May 1, 1995): 1385. http://dx.doi.org/10.1090/s0002-9939-1995-1264815-0.

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38

Girela, Daniel, José Ángel Peláez, Fernando Pérez-González, and Jouni Rättyä. "Carleson Measures for the Bloch Space." Integral Equations and Operator Theory 61, no. 4 (July 25, 2008): 511–47. http://dx.doi.org/10.1007/s00020-008-1602-9.

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39

Su, Jianbing, and Chao Zhang. "Composition Operators from p-Bloch Space to q-Bloch Space on the Fourth Cartan-Hartogs Domains." Journal of Operators 2015 (October 26, 2015): 1–10. http://dx.doi.org/10.1155/2015/718257.

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We obtain new generalized Hua’s inequality corresponding to YIV(N,n;K), where YIV(N,n;K) denotes the fourth Cartan-Hartogs domain in CN+n. Furthermore, we introduce the weighted Bloch spaces on YIV(N,n;K) and apply our inequality to study the boundedness and compactness of composition operator Cϕ from βp(YIV(N,n;K)) to βq(YIV(N,n;K)) for p≥0 and q≥0.
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40

Zhuo, Zhengyuan, and Shanli Ye. "Volterra-type operators from analytic Morrey spaces to Bloch space." Journal of Integral Equations and Applications 27, no. 2 (June 2015): 289–309. http://dx.doi.org/10.1216/jie-2015-27-2-289.

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41

Aulaskari, Rauno, Maria Nowak, and Ruhan Zhao. "The n-th derivative characterisation of Möbius invariant Dirichlet space." Bulletin of the Australian Mathematical Society 58, no. 1 (August 1998): 43–56. http://dx.doi.org/10.1017/s0004972700031993.

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In this paper we give the n-th derivative criterion for functions belonging to recently defined function spaces Qp and Qp, 0. For a special parameter value p = 1 this criterion is applied to BMOA and VMOA, and for p > 1 it is applied to the Bloch space and the little Bloch space . Further, a Carleson measure characterisation is given to Qp, and in the last section the multiplier space from Hq into Qp is considered.
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42

Ren, Guangbin, and Uwe Kähler. "WEIGHTED LIPSCHITZ CONTINUITY AND HARMONIC BLOCH AND BESOV SPACES IN THE REAL UNIT BALL." Proceedings of the Edinburgh Mathematical Society 48, no. 3 (September 15, 2005): 743–55. http://dx.doi.org/10.1017/s0013091502000020.

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43

Yuan, Cheng, and Cezhong Tong. "Distance from Bloch-Type Functions to the Analytic SpaceF(p,q,s)." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/610237.

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The analytic spaceF(p,q,s)can be embedded into a Bloch-type space. We establish a distance formula from Bloch-type functions toF(p,q,s), which generalizes the distance formula from Bloch functions to BMOA by Peter Jones, and toF(p,p-2,s)by Zhao.
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44

Liang, Yu-Xia, and Ya Wang. "New characterizations for differences of integral-type operators from α-Bloch space to β-Bloch-Orlicz space." Operators and Matrices, no. 2 (2021): 387–411. http://dx.doi.org/10.7153/oam-2021-15-27.

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45

Ye, Shanli. "Norm and Essential Norm of Composition Followed by Differentiation from Logarithmic Bloch Spaces toHμ∞." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/725145.

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In this note we express the norm of composition followed by differentiationDCφfrom the logarithmic Bloch and the little logarithmic Bloch spaces to the weighted spaceHμ∞on the unit disk and give an upper and a lower bound for the essential norm of this operator from the logarithmic Bloch space toHμ∞.
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46

Honda, Tatsuhiro. "Operators from the Hardy space to the α‐Bloch space." Mathematische Nachrichten 292, no. 10 (July 9, 2019): 2203–11. http://dx.doi.org/10.1002/mana.201700435.

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47

Liu, Junming, Zengjian Lou, and Ajay K. Sharma. "Weighted Differentiation Composition Operators to Bloch-Type Spaces." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/151929.

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We characterized the boundedness and compactness of weighted differentiation composition operators from BMOA and the Bloch space to Bloch-type spaces. Moreover, we obtain new characterizations of boundedness and compactness of weighted differentiation composition operators.
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48

Xu, Zhenghua. "Bloch type spaces on the unit ball of a Hilbert space." Czechoslovak Mathematical Journal 69, no. 3 (November 9, 2018): 695–711. http://dx.doi.org/10.21136/cmj.2018.0495-17.

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49

Bao, Guanlong, and Nihat Gökhan Göğüş. "On the Closures of Dirichlet Type Spaces in the Bloch Space." Complex Analysis and Operator Theory 13, no. 1 (April 24, 2017): 45–59. http://dx.doi.org/10.1007/s11785-017-0676-2.

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50

Fang, Zhong-Shan, and Ze-Hua Zhou. "Extended Cesáro operators from generally weighted Bloch spaces to Zygmund space." Journal of Mathematical Analysis and Applications 359, no. 2 (November 2009): 499–507. http://dx.doi.org/10.1016/j.jmaa.2009.06.013.

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