Besov spaces and Bergman projections on the ball

H.Turgay Kaptanoğlu

doi:10.1016/S1631-073X(02)02556-6

Besov spaces and Bergman projections on the ball
[Les espaces de Besov et les projections de Bergman dans la boule]

H.Turgay Kaptanoğlu ¹

¹ Mathematics Department, Middle East Technical University, Ankara 06531, Turkey

Comptes Rendus. Mathématique, Volume 335 (2002) no. 9, pp. 729-732.

Résumé
Abstract

Nous étudions une class d'opérateurs différentiels radiaux conduisant à une classification naturelle des espaces de Besov diagonaux dans la boule unité de $ℂ^{N}$ . Nous donnons les conditions précises pour la bornitude des projections de Bergman de certains espaces L^p sur des espaces de Besov. Nous déterminons aussi des inverses à droite pour ces projections. Nous présentons des applications à l'interpolation complexe.

A class of radial differential operators are investigated yielding a natural classification of diagonal Besov spaces on the unit ball of $ℂ^{N}$ . Precise conditions are given for the boundedness of Bergman projections from certain L^p spaces onto Besov spaces. Right inverses for these projections are also provided. Applications to complex interpolation are presented.

Reçu le : 2002-09-02
Accepté le : 2002-09-13
Publié le : 2002-10-01

DOI : 10.1016/S1631-073X(02)02556-6

Affiliations des auteurs :

H.Turgay Kaptanoğlu ¹

¹ Mathematics Department, Middle East Technical University, Ankara 06531, Turkey

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H.Turgay Kaptanoğlu. Besov spaces and Bergman projections on the ball. Comptes Rendus. Mathématique, Volume 335 (2002) no. 9, pp. 729-732. doi : 10.1016/S1631-073X(02)02556-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02556-6/

Bibliographie
Cité par

[1] J. Agler; J.E. McCarthy Complete Nevanlinna–Pick kernels, J. Funct. Anal., Volume 175 (2000), pp. 111-124

[2] D. Alpay; H.T. Kaptanoğlu Integral formulas for a sub-Hardy Hilbert space on the ball with complete Nevanlinna–Pick reproducing kernel, C. R. Acad. Sci. Paris, Série I, Volume 333 (2001), pp. 285-290

[3] D. Alpay; H.T. Kaptanoğlu Some-finite dimensional backward-shift-invariant subspaces in the ball and a related interpolation problem, Integral Equations Operator Theory, Volume 42 (2002), pp. 1-21

[4] D. Alpay, H.T. Kaptanoğlu, Gleason's problem and homogeneous interpolation in Hardy and Dirichlet-type spaces of the ball, J. Math. Anal. Appl., 2002, to appear

[5] J. Arazy Boundedness and compactness of generalized Hankel operators on bounded symmetric domains, J. Funct. Anal., Volume 137 (1996), pp. 97-151

[6] J. Arazy; S.D. Fisher; S. Janson; J. Peetre Membership of Hankel operators on the ball in unitary ideals, J. London Math. Soc., Volume 43 (1991), pp. 485-508

[7] J. Arazy; H. Upmeier Invariant inner product in spaces of holomorphic functions on bounded symmetric domains, Doc. Math., Volume 2 (1997), pp. 213-261

[8] J.A. Ball; T. Trent; V. Vinnikov Interpolation and commutant lifting for multipliers on reproducing kernel Hilbert spaces, Oper. Theory Adv. Appl., 122, Birkhäuser, Basel, 2001, pp. 89-138

[9] F. Beatrous; J. Burbea Holomorphic Sobolev spaces on the ball, Dissertationes Math., Volume 276 (1989)

[10] K.T. Hahn; E.H. Youssfi Möbius invariant Besov p-spaces and Hankel operators in the Bergman space on the ball in $ℂ^{n}$ , Complex Variables Theory Appl., Volume 17 (1991), pp. 89-104

[11] M.M. Peloso Möbius invariant spaces on the unit ball, Michigan Math. J., Volume 39 (1992), pp. 509-536

[12] K.E. Shaw Tangential limits and exceptional sets for holomorphic Besov functions in the unit ball of $ℂ^{n}$ , Illinois J. Math., Volume 37 (1993), pp. 171-185

[13] Z. Yan Invariant differential operators and holomorphic function spaces, J. Lie Theory, Volume 10 (2000), pp. 1-31

[14] K. Zhu Operator Theory in Function Spaces, Dekker, New York, 1990

[15] K. Zhu Holomorphic Besov spaces on bounded symmetric domains, I, Quart. J. Math. Oxford, Volume 46 (1995), pp. 239-256

[16] K. Zhu Holomorphic Besov spaces on bounded symmetric domains, II, Indiana Univ. Math. J., Volume 44 (1995), pp. 1017-1031

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Wenwan Yang; Xiao-Min Huang; Feifei Du Embedding and fractional embedding of Bergman-type spaces in the Schatten class, Applied Mathematics and Computation, Volume 472 (2024), p. 128628 | DOI:10.1016/j.amc.2024.128628
Wenwan Yang; Hanxing Lin; Cheng Yuan Small Hankel operators between Bergman-type spaces in the unit ball, Complex Variables and Elliptic Equations, Volume 69 (2024) no. 9, p. 1462 | DOI:10.1080/17476933.2023.2226060
H. Turgay Kaptanoğlu; A. Ersin Üreyen Precise inclusion relations among Bergman–Besov and Bloch–Lipschitz spaces and on the unit ball of, Mathematische Nachrichten, Volume 291 (2018) no. 14-15, p. 2236 | DOI:10.1002/mana.201700236
A. Ersin Üreyen Oscillation of holomorphic Bergman–Besov kernels on the ball, Monatshefte für Mathematik, Volume 184 (2017) no. 2, p. 297 | DOI:10.1007/s00605-017-1043-0
Kamthorn Chailuek; Brian C. Hall Toeplitz Operators on Generalized Bergman Spaces, Integral Equations and Operator Theory, Volume 66 (2010) no. 1, p. 53 | DOI:10.1007/s00020-009-1734-6
Ü. Aksoy; A.O. çelebi Schwarz problem for higher-order complex elliptic partial differential equations, Integral Transforms and Special Functions, Volume 19 (2008) no. 6, p. 413 | DOI:10.1080/10652460801933645
H. Turgay Kaptanoğlu Carleson measures for Besov spaces on the ball with applications, Journal of Functional Analysis, Volume 250 (2007) no. 2, p. 483 | DOI:10.1016/j.jfa.2006.12.016
Daniel Alpay; H.Turgay Kaptanoğlu Gleason's problem and homogeneous interpolation in Hardy and Dirichlet-type spaces of the ball, Journal of Mathematical Analysis and Applications, Volume 276 (2002) no. 2, p. 654 | DOI:10.1016/s0022-247x(02)00412-2

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