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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Directional derivative estimates for Berezin's operator calculus


Authors: L. A. Coburn and Bo Li
Journal: Proc. Amer. Math. Soc. 136 (2008), 641-649
MSC (2000): Primary 47B32; Secondary 32A36
Published electronically: November 2, 2007
MathSciNet review: 2358506
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Abstract: Directional derivative estimates for Berezin symbols of bounded operators on Bergman spaces of arbitrary bounded domains $ \Omega$ in $ \mathbb{C}^n$ are obtained. These estimates also hold in the setting of the Segal-Bargmann space on $ \mathbb{C}^n$. It is also shown that our estimates are sharp at every point of $ \Omega$ by exhibiting the optimizers explicitly.


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Additional Information

L. A. Coburn
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
Email: lcoburn@buffalo.edu

Bo Li
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
Email: boli@buffalo.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09081-8
PII: S 0002-9939(07)09081-8
Received by editor(s): September 21, 2006
Received by editor(s) in revised form: January 12, 2007
Published electronically: November 2, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society