Regularity of the Berezin Transform on the Elementary Reinhardt Domains

Abstract

In this paper, we consider a class of logarithmically convex domains in \({\mathbb {C}}^n\), called elementary Reinhardt domains, which can be regarded as a natural generalization of Hartogs triangles. The purpose of this paper is twofold. On one hand, we will compute the explicit forms of the Bergman kernel of weighted Hilbert space with radial symbols. On the other hand, by using the expressions of the weighted Bergman kernel, we will show the regularity of the Berezin transform on the elementary Reinhardt domains.