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Journal of Function Spaces and Applications
Volume 9 (2011), Issue 2, Pages 109-128
http://dx.doi.org/10.1155/2011/291620

L-Estimates of the Bergman projection in the Lie ball of n

University of Buea, Faculty of Science, Department of Mathematics, P.O. Box 63, Buea, Cameroon

Received 1 June 2009

Academic Editor: Miroslav Engliš

Copyright © 2011 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we consider estimates with loss for the Bergman projections of bounded symmetric domains of n in their Harish-Chandra realizations. This paper is twofold: on one side we develop transfer methods between these bounded domains and their Cayley transform; on the other side we give a new range of q such that the Bergman projection is bounded from L(n) to Lq(n) where n is the Lie ball of n.