Weighted composition operators from the Bloch space to weighted Banach spaces on bounded homogeneous domains

TL;DR

This paper investigates the properties of weighted composition operators from the Bloch space to weighted Banach spaces on bounded homogeneous domains, providing characterizations, norm estimates, and compactness criteria, especially for the unit polydisk.

Contribution

It offers a comprehensive characterization of bounded and compact weighted composition operators on bounded homogeneous domains and the unit polydisk, including operator norm calculations.

Findings

Characterization of bounded weighted composition operators.

Sufficient conditions for compactness.

Complete characterization and norm estimates for the unit polydisk.

Abstract

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide computable estimates on the operator norm.