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Comptes Rendus Mathématique
Volume 335, n° 9
pages 729-732 (novembre 2002)
Doi : S1631-073X(02)02556-6
Received : 2 September 2002 ;  accepted : 13 September 2002
Besov spaces and Bergman projections on the ball
Les espaces de Besov et les projections de Bergman dans la boule
 

H.Turgay Kaptanoğlu
Mathematics Department, Middle East Technical University, Ankara 06531, Turkey 

Note presented by Jean-Pierre Kahane

Abstract

A class of radial differential operators are investigated yielding a natural classification of diagonal Besov spaces on the unit ball of CN. Precise conditions are given for the boundedness of Bergman projections from certain Lp spaces onto Besov spaces. Right inverses for these projections are also provided. Applications to complex interpolation are presented. To cite this article: H.T. Kaptanoğlu, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 729-732.

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Résumé

Nous étudions une class d'opérateurs différentiels radiaux conduisant à une classification naturelle des espaces de Besov diagonaux dans la boule unité de CN. Nous donnons les conditions précises pour la bornitude des projections de Bergman de certains espaces Lp sur des espaces de Besov. Nous déterminons aussi des inverses à droite pour ces projections. Nous présentons des applications à l'interpolation complexe. Pour citer cet article : H.T. Kaptanoğlu, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 729-732.

The full text of this article is available in PDF format.


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