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Article: Commutativity of the Berezin transform of the pluriharmonic functions.
- Article from:
- Global Journal of Pure and Applied Mathematics
- Article date:
- April 1, 2007
- Author:
CopyrightCOPYRIGHT 2007 Research India Publications. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract
Let B be the open unit ball in the n-space [C.sup.n] and [T.sub.u] be the Toeplitz operator on the Bergman space [L.sup.2.sub.a](B) with symbol u. For u [member of] [L.sup.[infinity]], the Berezin transform of u, is denoted by [??] and is defined as [??](z) =
<[T.sub.u][k.sub.z]; [k.sub.z]>. In the present paper we discuss the multiplication and commutativity of the Berezin transform of the pluriharmonic functions.
AMS Subject Classification: Primary 47B35, 47B05.
Keywords and Phrases: Berezin transform, pluriharmonic functions, Bergman spaces.
1. Introduction
Let dv denote the normalized volume measure on the open unit ball B in the space ...