The Berezin transform and Laplace-Beltrami operator

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:327

Article

Li, Bo

关键词: Berezin transform;    Laplace-Beltrami operator;    Bergman space;   

DOI  :  10.1016/j.jmaa.2006.04.068

来源: Elsevier

【 摘 要 】

We study the Berezin transform of bounded operators on the Bergman space on a bounded symmetric domain Omega in C-n. The invariance of range of the Berezin transform with respect to G = Aut(Omega), the automorphism group of biholomorphic maps on Omega, is derived based on the general framework on invariant symbolic calculi on symmetric domains established by Arazy and Upmeier. Moreover we show that as a smooth bounded function, the Berezin transform of any bounded operator is also bounded under the action of the algebra of invariant differential operators generated by the Laplace-Beltrami operator on the unit disk and even on the unit ball of higher dimensions. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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