Difference of composition-differentiation operators from Hardy spaces to weighted Bergman spaces via harmonic analysis

TL;DR

This paper characterizes when the difference of composition-differentiation operators from Hardy spaces to weighted Bergman spaces is bounded or compact, using harmonic analysis techniques.

Contribution

It provides a complete characterization of boundedness and compactness for these operators across all relevant parameters.

Findings

Complete characterization of boundedness conditions.

Complete characterization of compactness conditions.

Applicable to all 0<p,q<∞ cases.

Abstract

In this paper, the boundedness and compactness of the difference of composition-differentiation operators $D_\varphi-D_\psi$ acting from Hardy spaces $H^p$ to weighted Bergman spaces $A^q_\alpha$ are completely characterize for all $0<p,q<\infty$.