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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Directional derivative estimates for Berezin’s operator calculus
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by L. A. Coburn and Bo Li PDF
Proc. Amer. Math. Soc. 136 (2008), 641-649 Request permission

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
  • 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
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 641-649
  • MSC (2000): Primary 47B32; Secondary 32A36
  • DOI: https://doi.org/10.1090/S0002-9939-07-09081-8
  • MathSciNet review: 2358506