Positive Toeplitz operators on weighted Bergman spaces of a minimal bounded homogeneous domain

Abstract

We give criteria for the boundedness of positive Toeplitz operators on weighted Bergman spaces of a minimal bounded homogeneous domain in terms of the Berezin symbol or the averaging function of the symbol. Moreover, we estimate the essential norm of positive Toeplitz operators assuming that they are bounded. As an application of these estimates, we also give necessary and sufficient conditions for the positive Toeplitz operators to be compact.