A Note on the Berezin Transform of Harmonic Functions
by
S. Mansour Vaezpour
Dept. of Math., Yazd University, Iran

Let A be a bounded operator on a Hilbert space of analytic functions on D. The Berezin transform of A is defined by [A\tilde](z)= < Ak_z, k_z > for every z in D, where k_z is the normalized reproducing kernel. For f in L^\infty define [f\tilde]=[T\tilde]_f, where T_f is the Toeplitz operator with symbol f. In this paper we characterize those harmonic functions for which their Berezin Transforms are multiplicative or commutative.

Date received: August 9, 2000