Composition operators on the Bergman spaces of a minimal bounded homogeneous domain

TL;DR

This paper characterizes when composition operators are compact on weighted Bergman spaces of minimal bounded homogeneous domains, using integral formulas and boundary behavior of the Bergman kernel.

Contribution

It provides a necessary and sufficient condition for the compactness of composition operators on these spaces, based on boundary analysis.

Findings

Derived integral formula on homogeneous Siegel domain

Established boundary behavior criteria for the Bergman kernel

Provided a complete characterization of compactness for composition operators

Abstract

Using an integral formula on a homogeneous Siegel domain, we show a necessary and sufficient condition for composition operators on the weighted Bergman space of a minimal bounded homogeneous domain to be compact. To describe the compactness of composition operators, we see a boundary behavior of the Bergman kernel.