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5th International ISAAC Congress
July 25-30, 2005
Department of Mathematics and Informatics, University of Catania
Catania, Sicily, Italy

Organizers
International ISAAC Board, Local organizing committee: F. Nicolosi (chairman), S. Bonafede, V. Cataldo, P. Cianci, G.R. Cirmi, S. D'Asero, G. Fiorito, L. Giusti, S. Leonardi, P.E. Ricci

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Carleson Measures for Besov Spaces on the Ball
by
H. Turgay Kaptanoglu
Middle East Technical University

Carleson and vanishing Carleson measures for Besov spaces on the unit ball of CN are characterized in terms of Berezin transforms and Bergman-metric balls. The measures are defined via natural imbeddings of Besov spaces into Lebesgue classes by certain combinations of radial derivatives. Membership in Schatten classes of the imbeddings is considered too. Some Carleson measures are not finite, but the results extend those known for weighted Bergman spaces. Special cases pertain to Arveson and Dirichlet spaces, and the usual Hardy-space Carleson measures are obtained as the order of the radial derivatives tends to 0. Weak convergence in Besov spaces are also characterized, and weakly 0-convergent families are exhibited. Carleson measures are applied to descriptions of functions in weighted Bloch spaces.

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Date received: May 7, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqw-20.