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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Berezin transform and $ m$th-order Bergman metric


Author: Bo Li
Journal: Trans. Amer. Math. Soc. 363 (2011), 3031-3056
MSC (2010): Primary 47B32; Secondary 32F45, 32A36
Published electronically: January 27, 2011
MathSciNet review: 2775797
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Abstract: We improve upon recent directional derivative estimates for Berezin's operator calculus, and consider the relation between the $ m$th-order Bergman metric of Burbea and the classical Bergman metric in the analysis of higher order directional derivative estimates of the Berezin symbols of general bounded operators. A new metric, naturally arising in our analysis, is introduced and certain comparison theorems are established among this metric, the $ m$th-order Bergman metric and the classical Bergman metric on the unit ball, the polydisk and $ \mathbb{C}^n$.


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Additional Information

Bo Li
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
Address at time of publication: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05063-4
PII: S 0002-9947(2011)05063-4
Received by editor(s): March 21, 2008
Received by editor(s) in revised form: March 30, 2009
Published electronically: January 27, 2011
Additional Notes: The main part of this paper appeared in the author’s Ph.D. dissertation at State University of New York at Buffalo.
Article copyright: © Copyright 2011 American Mathematical Society