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Comptes Rendus Mathématique
Volume 343, n° 7
pages 453-456 (octobre 2006)
Doi : 10.1016/j.crma.2006.09.001
Received : 30 January 2006 ;  accepted : 5 September 2006
Besov spaces and Carleson measures on the ball
Les espaces de Besov et les mesures de Carleson dans la boule
 

H. Turgay Kaptanoğlu 1
Department of Mathematics, Bilkent University, Ankara 06800, Turkey 

Abstract

Carleson and vanishing Carleson measures for Besov spaces on the unit ball of   are defined using imbeddings into Lebesgue classes via radial derivatives. The measures, some of which are infinite, are characterized in terms of Berezin transforms and Bergman-metric balls, extending results for weighted Bergman spaces. Special cases pertain to Arveson and Dirichlet spaces, and a unified view with the Hardy-space Carleson measures are presented. Weak convergence in Besov spaces is characterized, and weakly 0-convergent families are exhibited. Carleson measures are applied to characterizations of functions in weighted Bloch and Lipschitz spaces. To cite this article: H.T. Kaptanoğlu, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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Résumé

Utilisant les inclusions dans les espaces de Lebesgue à lʼaide des dérivées radiales nous définissons les mesures de Carleson et les mesures de Carleson évanescentes dans le cadre des espaces de Besov de la boule unité de  . Ces mesures (certaines dʼentre elles sont infinies) sont caractérisées à lʼaide des transformées de Berezin et de boules dans la métrique de Bergman, ce qui nous permet dʼétendre les résultats des espaces de Bergman avec poids. Notons les cas particuliers des espaces dʼArveson et de Dirichlet. Nous présentons un point de vue unifié avec les mesures de Carleson des espaces de Hardy. La convergence faible dans les espaces de Besov est caractérisée et nous donnons des exemples de familles qui convergent faiblement vers 0. Les mesures de Carleson sont utilisées pour caractériser les éléments des espaces de Bloch avec poids et des espaces de Lipschitz. Pour citer cet article : H.T. Kaptanoğlu, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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1  The research of the author is partially supported by a Fulbright grant.


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