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Journal articles on the topic 'Bergman spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 March 2023

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1

Alhami, Kifah Y. "OPERATORS ON BERGMAN SPACES." Journal of Southwest Jiaotong University 56, no. 5 (October 30, 2021): 399–403. http://dx.doi.org/10.35741/issn.0258-2724.56.5.35.

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Bergman space theory has been at the core of complex analysis research for many years. Indeed, Hardy spaces are related to Bergman spaces. The popularity of Bergman spaces increased when functional analysis emerged. Although many researchers investigated the Bergman space theory by mimicking the Hardy space theory, it appeared that, unlike their cousins, Bergman spaces were more complex in different aspects. The issue of invariant subspace constitutes one common problem in mathematics that is yet to be resolved. For Hardy spaces, each invariant subspace for shift operators features an elegant description. However, the method for formulating particular structures for the large invariant subspace of shift operators upon Bergman spaces is still unknown. This paper aims to characterize bounded Hankel operators involving a vector-valued Bergman space compared to other different vector value Bergman spaces.

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2

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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3

Ghiloufi, N., and M. Zaway. "Meromorphic Bergman spaces." Ukrains’kyi Matematychnyi Zhurnal 74, no. 8 (October 4, 2022): 1060–72. http://dx.doi.org/10.37863/umzh.v74i8.6163.

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UDC 517.5We introduce new spaces of holomorphic functions on the pointed unit disc in <em>C</em> that generalize classical Bergman spaces. We prove some fundamental properties of these spaces and their dual spaces. Finally, we extend the Hardy – Littlewood and Fejer – Riesz inequalities to these spaces with application of the Toeplitz operators. ´

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4

Vasilevski1, N. L. "On quaternionic bergman and poly-bergman spaces." Complex Variables, Theory and Application: An International Journal 41, no. 2 (April 2000): 111–32. http://dx.doi.org/10.1080/17476930008815241.

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5

Shamoyan, Romi F., and Olivera Mihić. "On Extremal Problems in Certain New Bergman Type Spaces in Some Bounded Domains inCn." Journal of Function Spaces 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/975434.

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Based on recent results on boundedness of Bergman projection with positive Bergman kernel in analytic spaces in various types of domains inCn, we extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new Bergman type spaces in Lie ball, bounded symmetric domains of tube type, Siegel domains, and minimal bounded homogeneous domains.

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6

Peláez, José Ángel, Jouni Rättyä, and Kian Sierra. "Embedding Bergman spaces into tent spaces." Mathematische Zeitschrift 281, no. 3-4 (September 19, 2015): 1215–37. http://dx.doi.org/10.1007/s00209-015-1528-2.

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7

Shamoyan, Romi F., and Olivera R. Mihić. "On some extremal problems in Bergman spaces in weakly pseudoconvex domains." Communications in Mathematics 26, no. 2 (December 1, 2018): 83–97. http://dx.doi.org/10.2478/cm-2018-0006.

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AbstractWe consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂn based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces $A_\alpha ^p$ in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.

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8

Axler, Sheldon. "Zero Multipliers of Bergman Spaces." Canadian Mathematical Bulletin 28, no. 2 (June 1, 1985): 237–42. http://dx.doi.org/10.4153/cmb-1985-029-1.

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9

Lusky, Wolfgang. "On generalized Bergman spaces." Studia Mathematica 119, no. 1 (1996): 77–95. http://dx.doi.org/10.4064/sm-119-1-77-95.

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10

Rochberg, Richard. "Book Review: Bergman spaces." Bulletin of the American Mathematical Society 42, no. 02 (January 12, 2005): 251–57. http://dx.doi.org/10.1090/s0273-0979-05-01046-3.

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11

Chacón, Gerardo R., and Humberto Rafeiro. "Variable exponent Bergman spaces." Nonlinear Analysis: Theory, Methods & Applications 105 (August 2014): 41–49. http://dx.doi.org/10.1016/j.na.2014.04.001.

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12

Békollé, David. "Theory of Bergman Spaces." Mathematical Intelligencer 27, no. 1 (December 2005): 85–86. http://dx.doi.org/10.1007/bf02984819.

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13

Sultanic, Saida. "Sub-Bergman Hilbert spaces." Journal of Mathematical Analysis and Applications 324, no. 1 (December 2006): 639–49. http://dx.doi.org/10.1016/j.jmaa.2005.12.035.

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14

Zabulionis, A. "Imbedding of Bergman spaces." Lithuanian Mathematical Journal 27, no. 2 (1988): 123–28. http://dx.doi.org/10.1007/bf00966193.

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15

BÁRTA, TOMÁŠ. "ON R-SECTORIAL DERIVATIVES ON BERGMAN SPACES." Bulletin of the Australian Mathematical Society 77, no. 2 (April 2008): 305–13. http://dx.doi.org/10.1017/s0004972708000324.

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AbstractIn this paper we show boundedness of vector-valued Bergman projections on simple connected domains. With this result we show R-sectoriality of the derivative on the Bergman space on C+ and maximal Lp-regularity for an integrodifferential equation with a kernel in the Bergman space.

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16

Chen, Zeqian, and Wei Ouyang. "Maximal and Area Integral Characterizations of Bergman Spaces in the Unit Ball ofℂn." Journal of Function Spaces and Applications 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/167514.

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We present maximal and area integral characterizations of Bergman spaces in the unit ball ofℂn. The characterizations are in terms of maximal functions and area integral functions on Bergman balls involving the radial derivative, the complex gradient, and the invariant gradient. As an application, we obtain new maximal and area integral characterizations of Besov spaces. Moreover, we give an atomic decomposition of real-variable type with respect to Carleson tubes for Bergman spaces.

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17

Luecking, Daniel H. "Multipliers of Bergman spaces into Lebesgue spaces." Proceedings of the Edinburgh Mathematical Society 29, no. 1 (February 1986): 125–31. http://dx.doi.org/10.1017/s001309150001748x.

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Let U be the open unit disk in the complex plane endowed with normalized Lebesgue measure m. will denote the usual Lebesgue space with respect to m, with 0<p<+∞. The Bergman space consisting of the analytic functions in will be denoted . Let μ be some positivefinite Borel measure on U. It has been known for some time (see [6] and [9]) what conditions on μ are equivalent to the estimate: There is a constant C such thatprovided 0<p≦q.

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18

Cho, Hong Rae, and Jinkee Lee. "On boundedness of the weighted Bergman projections on the Lipschitz spaces." Bulletin of the Australian Mathematical Society 66, no. 3 (December 2002): 385–91. http://dx.doi.org/10.1017/s0004972700040247.

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19

Vasilevski, N. L. "On the structure of Bergman and poly-Bergman spaces." Integral Equations and Operator Theory 33, no. 4 (December 1999): 471–88. http://dx.doi.org/10.1007/bf01291838.

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20

Selvan, A. Antony, and R. Radha. "Frames in Hermite-Bergman and special Hermite-Bergman spaces." Journal of Pseudo-Differential Operators and Applications 8, no. 2 (November 3, 2016): 241–54. http://dx.doi.org/10.1007/s11868-016-0178-4.

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21

BUCKLEY, STEPHEN M., PEKKA KOSKELA, and DRAGAN VUKOTIĆ. "Fractional integration, differentiation, and weighted Bergman spaces." Mathematical Proceedings of the Cambridge Philosophical Society 126, no. 2 (March 1999): 369–85. http://dx.doi.org/10.1017/s030500419800334x.

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We study the action of fractional differentiation and integration on weighted Bergman spaces and also the Taylor coeffficients of functions in certain subclasses of these spaces. We then derive several criteria for the multipliers between such spaces, complementing and extending various recent results. Univalent Bergman functions are also considered.

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22

Shamoyan, Romi F., and Olivera R. Mihić. "On Distance Function in Some New Analytic Bergman Type Spaces inℂn." Journal of Function Spaces 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/275416.

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We extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new analytic Bergman type spaces in higher dimensions inℂn. Also, we study the same problem in anisotropic mixed normh(p,q,s)spaces consisting ofn-harmonic functions on the unit polydisc ofℂn.

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23

Stroethoff, Karel. "Compact Toeplitz operators on weighted harmonic Bergman spaces." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 64, no. 1 (February 1998): 136–48. http://dx.doi.org/10.1017/s144678870000135x.

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AbstractWe consider the Bergman spaces consisting of harmonic functions on the unit ball in Rn that are squareintegrable with respect to radial weights. We will describe compactness for certain classes of Toeplitz operators on these harmonic Bergman spaces.

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24

Guo, Xin, and Maofa Wang. "Compact linear combinations of composition operators over the unit ball." Journal of Operator Theory 88, no. 1 (June 15, 2022): 61–84. http://dx.doi.org/10.7900/jot.2020nov28.2310.

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In this paper, we study the compactness of any finite linear combination of composition operators with general symbols on weighted Bergman spaces over the unit ball in terms of a power type criterion. The strategy of the proof involves the subtle connection of composition operator theory between weighted Bergman spaces and Korenblum spaces.

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25

Clifford, J. H., and Dechao Zheng. "Composition Operators on Bergman Spaces." Chinese Annals of Mathematics 24, no. 04 (October 2003): 433–48. http://dx.doi.org/10.1142/s0252959903000438.

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26

Bekolle, David. "Bergman spaces with small exponents." Indiana University Mathematics Journal 49, no. 3 (2000): 0. http://dx.doi.org/10.1512/iumj.2000.49.1687.

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27

Stević, Stevo. "On generalized weighted bergman spaces." Complex Variables, Theory and Application: An International Journal 49, no. 2 (February 10, 2004): 109–24. http://dx.doi.org/10.1080/02781070310001650047.

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28

Bertram, Wolfgang, and Joachim Hilgert. "Geometric Hardy and Bergman spaces." Michigan Mathematical Journal 47, no. 2 (2000): 235–63. http://dx.doi.org/10.1307/mmj/1030132532.

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29

Wu, Zhijian. "Operators on harmonic Bergman spaces." Integral Equations and Operator Theory 24, no. 3 (September 1996): 352–71. http://dx.doi.org/10.1007/bf01204606.

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30

Miao, Jie, and Dechao Zheng. "Compact Operators on Bergman Spaces." Integral Equations and Operator Theory 48, no. 1 (January 1, 2004): 61–79. http://dx.doi.org/10.1007/s00020-002-1176-x.

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31

Wu, Zhijian. "Area operator on Bergman spaces." Science in China Series A 49, no. 7 (July 2006): 987–1008. http://dx.doi.org/10.1007/s11425-006-0987-7.

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32

Hu, Zhangjian, Xiaofen Lv, and Alexander P. Schuster. "Bergman spaces with exponential weights." Journal of Functional Analysis 276, no. 5 (March 2019): 1402–29. http://dx.doi.org/10.1016/j.jfa.2018.05.001.

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33

Akgün, R. "Polynomial Approximation in Bergman Spaces." Ukrainian Mathematical Journal 68, no. 4 (September 2016): 485–501. http://dx.doi.org/10.1007/s11253-016-1236-z.

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34

Faour, Nazih S. "Toeplitz operators on Bergman spaces." Rendiconti del Circolo Matematico di Palermo 35, no. 2 (June 1986): 221–32. http://dx.doi.org/10.1007/bf02844733.

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35

Chen, Sh, S. Ponnusamy, and X. Wang. "Harmonic mappings in Bergman spaces." Monatshefte für Mathematik 170, no. 3-4 (November 15, 2012): 325–42. http://dx.doi.org/10.1007/s00605-012-0448-z.

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36

Aleman, Alexandru, Stefan Richter, and William T. Ross. "Bergman Spaces on Disconnected Domains." Canadian Journal of Mathematics 48, no. 2 (April 1, 1996): 225–43. http://dx.doi.org/10.4153/cjm-1996-011-5.

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AbstractFor a bounded region G ⊂ ℂ and a compact set K ⊂ G, with area measure zero, we will characterize the invariant subspaces ℳ (under ƒ → zƒ) of the Bergman space (G \ K), 1 ≤ p < ∞, which contain (G) and with dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K. When G \ K is connected, we will see that dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K and thus in this case we will have a complete description of the invariant subspaces lying between (G) and (G \ K). When p = ∞, we will remark on the structure of the weak-star closed z-invariant subspaces between H∞(G) and H∞(G \ K). When G \ K is not connected, we will show that in general the invariant subspaces between (G) and (G \ K) are fantastically complicated. As an application of these results, we will remark on the complexity of the invariant subspaces (under ƒ → ζƒ) of certain Besov spaces on K. In particular, we shall see that in the harmonic Dirichlet space , there are invariant subspaces ℱ such that the dimension of ζℱ in ℱ is infinite.

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37

Aleman, Alexandru, and Aristomenis G. Siskakis. "Integration operators on Bergman spaces." Indiana University Mathematics Journal 46, no. 2 (1997): 0. http://dx.doi.org/10.1512/iumj.1997.46.1373.

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38

Luecking, Daniel H. "Zero sequences for bergman spaces." Complex Variables, Theory and Application: An International Journal 30, no. 4 (August 1996): 345–62. http://dx.doi.org/10.1080/17476939608814936.

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39

Andersson, Mats Erik. "Integral means on bergman spaces." Complex Variables, Theory and Application: An International Journal 32, no. 2 (March 1997): 147–60. http://dx.doi.org/10.1080/17476939708814985.

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40

Sadraoui, Houcine. "Hyponormality on general Bergman spaces." Filomat 33, no. 17 (2019): 5737–41. http://dx.doi.org/10.2298/fil1917737s.

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A bounded operator T on a Hilbert space is hyponormal if T*T-TT* is positive. We give a necessary condition for the hyponormality of Toeplitz operators on weighted Bergman spaces, for a certain class of radial weights, when the symbol is of the form f+g?, where both functions are analytic and bounded on the unit disk. We give a sufficient condition when f is a monomial.

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41

Diamantopoulos, E. "Hilbert matrix on Bergman spaces." Illinois Journal of Mathematics 48, no. 3 (July 2004): 1067–78. http://dx.doi.org/10.1215/ijm/1258131071.

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42

Chakrabarti, Debraj, and Pranav Upadrashta. "Fourier representations in Bergman spaces." Journal of Mathematical Analysis and Applications 475, no. 1 (July 2019): 464–89. http://dx.doi.org/10.1016/j.jmaa.2019.02.050.

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43

Shamoyan, R. F., and E. B. Tomashevskaya. "On some new sharp embedding theorems for multifunctional Herz-type and Bergman-type spaces in tubular domains over symmetric cones." REPORTS ADYGE (CIRCASSIAN) INTERNATIONAL ACADEMY OF SCIENCES 21, no. 3 (2021): 21–33. http://dx.doi.org/10.47928/1726-9946-2021-21-3-21-33.

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We introduce new multifunctional mixed norm analytic Herz-type spaces in tubular domains over symmetric cones and provide new sharp embedding theorems for them. Some results are new even in case of onefunctional holomorphic spaces. Some new related sharp results for new multifunctional Bergman-type spaces will be also provided under one condition on Bergman kernel.

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44

Arsenovic, Milos, and Romi Shamoyan. "Embedding relations and boundedness of the multifunctional operators in tube domains over symmetric cones." Filomat 25, no. 4 (2011): 109–26. http://dx.doi.org/10.2298/fil1104109a.

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We obtain a new general sufficient condition for the continuity of the Bergman projection in tube domains over symmetric cones using multifunctional embeddings. We also obtain some sharp embedding relations between the generalized Hilbert-Hardy spaces and the mixed-norm Bergman spaces in this setting.

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45

Bertram, Wolfgang, and Joachim Hilgert. "Hardy spaces and analytic continuation of Bergman spaces." Bulletin de la Société mathématique de France 126, no. 3 (1998): 435–82. http://dx.doi.org/10.24033/bsmf.2332.

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46

Hilgert, Joachim, and Bernhard Krötz. "Weighted Bergman spaces¶associated with causal symmetric spaces." manuscripta mathematica 99, no. 2 (June 1, 1999): 151–80. http://dx.doi.org/10.1007/s002290050167.

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47

Zhu, Xiangling, and Weifeng Yang. "Differences of composition operators from weighted Bergman spaces to Bloch spaces." Filomat 28, no. 9 (2014): 1935–41. http://dx.doi.org/10.2298/fil1409935z.

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48

SEHBA, BENOÎT F. "-CARLESON MEASURES AND MULTIPLIERS BETWEEN BERGMAN–ORLICZ SPACES OF THE UNIT BALL OF." Journal of the Australian Mathematical Society 104, no. 1 (March 22, 2017): 63–79. http://dx.doi.org/10.1017/s1446788717000076.

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We define the notion of $\unicode[STIX]{x1D6F7}$-Carleson measures, where $\unicode[STIX]{x1D6F7}$ is either a concave growth function or a convex growth function, and provide an equivalent definition. We then characterize $\unicode[STIX]{x1D6F7}$-Carleson measures for Bergman–Orlicz spaces and use them to characterize multipliers between Bergman–Orlicz spaces.

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49

Shamoyan, Romi, and Olivera Mihic. "On some new sharp embedding theorems for multifunctional Herz-type and Bergman-type spaces in pseudoconvex domains." Filomat 33, no. 17 (2019): 5677–90. http://dx.doi.org/10.2298/fil1917677s.

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We introduce new multifunctional mixed norm analytic Herz-type spaces in strongly pseudoconvex domains and provide new sharp embedding theorems for them. Some results are new even in case of onefunctional holomorphic spaces. Some new related sharp results for new multifunctional Bergman-type spaces will be also provided under one condition on Bergman kernel. Similar results with similar proofs in unbounded tubular domains over symmetric cones and bounded symmetric domains will be also shortly mentioned.

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50

Chacón, Gerardo R. "Toeplitz Operators on Weighted Bergman Spaces." Journal of Function Spaces and Applications 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/753153.

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