Difference of weighted composition operators on weighted-type spaces in the unit ball

TL;DR

This paper characterizes the boundedness, compactness, and essential norm of the difference between two weighted composition operators on weighted-type spaces within the unit ball in complex n-dimensional space.

Contribution

It introduces a new characterization for these operator differences, advancing understanding of their properties in weighted-type spaces.

Findings

Provides criteria for boundedness and compactness

Determines the essential norm of the operator difference

Enhances understanding of weighted composition operators in complex analysis

Abstract

In this paper, a new characterization is provided for the boundedness, compactness and essential norm of the difference of two weighted composition operators on weighted-type spaces in the unit ball of $\mathbb{C}^n$.