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.

Abstract (VO)
Résumé

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.

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.

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/

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W. Yang; C. Yuan Integral operators and Carleson measures for Möbius invariant Besov spaces, Analysis Mathematica, Volume 50 (2024) no. 2, pp. 683-716 | DOI:10.1007/s10476-024-00029-6 | Zbl:7915697
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Kamthorn Chailuek; Brian C. Hall Toeplitz operators on generalized Bergman spaces, Integral Equations and Operator Theory, Volume 66 (2010) no. 1, pp. 53-77 | DOI:10.1007/s00020-009-1734-6 | Zbl:1202.47029
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H. Turgay Kaptanoğlu Carleson measures for Besov spaces on the ball with applications, Journal of Functional Analysis, Volume 250 (2007) no. 2, pp. 483-520 | DOI:10.1016/j.jfa.2006.12.016 | Zbl:1135.46014
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