Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Sharp Berezin Lipschitz estimates

Author: L. A. Coburn
Journal: Proc. Amer. Math. Soc. 135 (2007), 1163-1168
MSC (2000): Primary 47B32; Secondary 32A36
Published electronically: October 13, 2006
MathSciNet review: 2262921
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Abstract: F.A. Berezin introduced a general ``symbol calculus" for linear operators on reproducing kernel Hilbert spaces. For the Segal-Bargmann space $ H^2({\text{\bf C}}^n,d\mu )$ of Gaussian square-integrable entire functions on complex $ n$-space, $ {\text{\bf C}}^n$, or for the Bergman spaces $ A^2 (\Omega)$ of Euclidean volume square-integrable holomorphic functions on bounded domains $ \Omega$ in $ {\text{\bf C}}^n$, we show here that earlier Lipschitz estimates for Berezin symbols of arbitrary bounded operators are sharp.

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L. A. Coburn
Affiliation: Department of Mathematics, SUNY at Buffalo, Buffalo, New York 14260

Received by editor(s): October 18, 2005
Received by editor(s) in revised form: November 15, 2005
Published electronically: October 13, 2006
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society