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On Burbea's mth order Bergman "metric" and Berezin's operator calculus
by
Bo Li
State University of New York at Buffalo
I consider the relation between Burbea's mth order Bergman "metric" Bm(z, v) and the classical Bergman metric B1(z, v) on bounded domains in Cn, and establish that Bm(z, v) is a constant multiple of B1(z, v)m on the open unit ball of Cn. As an application to Berezin's operator calculus, I show that functions on the unit ball which are in the range of the Berezin transform satisfy Bloch-type differential inequalities of all orders.
Date received: February 2, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavq-32.