Commutativity of the Berezin Transform of the Pluriharmonic Functions
Abstract
Let B be the open unit ball in the n-space Cn and Tu be the Toeplitz operator on the Bergman space (B) with symbol u. For u∈L∞, the Berezin transform of u, is denoted by ũ and is defined as ũ (z) = <Tukz, kz>. In the present paper we discuss the multiplication and commutativity of the Berezin transform of the pluriharmonic functions.
Keywords
Berezin transform, pluriharmonic functions, Bergman spaces