Weighted Berezin transformations with application to Toeplitz operators of Schatten class on parabolic Bergman spaces

Abstract

In the setting of α-parabolic Bergman spaces, we consider weighted versions of averaging functions and Berezin transformations. Related norm equivalence relations are shown. They are very useful to study our Bergman spaces. As an application, we characterize the Schatten classes of compact Toeplitz operators.