Difference of composition operators on Korenblum spaces over tube domain

TL;DR

This paper studies the difference of composition operators on Korenblum spaces over tube domains, characterizing their boundedness and compactness, and showing bounded differences are absolutely summable operators.

Contribution

It provides a new characterization of bounded and compact differences of composition operators on Korenblum spaces over tube domains.

Findings

Bounded differences are absolutely summable operators.

Characterization of boundedness and compactness of composition operator differences.

Analysis over the product of upper half planes.

Abstract

The Korenblum space, often referred to as a growth space, is a special type of analytic function space. This paper investigates the properties of the difference of composition operators on the Korenblum space over the product of upper half planes, characterizing their boundedness and compactness. Using the result on boundedness, we show that all bounded differences of composition operators are absolutely summable operators.