Weighted composition operators between weighted Hardy spaces on rooted trees

TL;DR

This paper introduces discrete weighted Hardy spaces on rooted trees and thoroughly investigates the properties of weighted composition operators, including boundedness, compactness, and isometries, within this new framework.

Contribution

It develops a novel discrete analogue of weighted Hardy spaces on rooted trees and characterizes various properties of weighted composition operators acting on them.

Findings

Characterization of bounded weighted composition operators

Criteria for compactness of these operators

Conditions for isometric weighted composition operators

Abstract

In this paper, we introduce a discrete analogue of weighted Hardy spaces on rooted trees and study weighted composition operators between them in detail. In particular, we characterize bounded and compact weighted composition operators between discrete Hardy spaces. We also consider isometric weighted composition operators between these spaces.