Weighted composition operators on the Bloch space of a bounded homogeneous domain

TL;DR

This paper investigates the properties of weighted composition operators on the Bloch space within bounded homogeneous domains in complex space, focusing on their boundedness, compactness, and mappings to Hardy spaces.

Contribution

It provides new results on the boundedness and compactness criteria for these operators and explores their behavior from the Bloch space to Hardy spaces.

Findings

Characterization of bounded weighted composition operators

Criteria for compactness of these operators

Analysis of operators mapping to Hardy space H^

Abstract

In this paper, we present the current results in the study of weighted composition operators on the Bloch space of bounded homogeneous domains in $\mathbb{C}^n$ with particular emphasis on the issues of boundedness and compactness. We also discuss the bounded and the compact weighted composition operators from the Bloch space to the Hardy space $H^\infty$.