Boundedness and compactness of weighted composition operators and monomial operators

TL;DR

This paper characterizes when certain monomial operators are bounded or compact by relating them to weighted composition operators and establishing explicit Carleson measure conditions on the half-plane.

Contribution

It introduces a new characterization of Agler--McCarthy monomial operators' boundedness and compactness via reduction to weighted composition operators and explicit measure criteria.

Findings

Derived explicit Carleson measure criteria for boundedness and compactness.

Reduced monomial operators to weighted composition operators for analysis.

Provided illustrative examples demonstrating the criteria.

Abstract

This paper characterises the boundedness and compactness of Agler--McCarthy monomial operators by reducing them to weighted composition operators and deriving explicit Carleson measure criteria on the half-plane. The results are illustrated by examples.