Differences of weighted differentiation composition operators from Bloch-type space to weighted-type space

TL;DR

This paper characterizes the boundedness and compactness of differences of weighted differentiation composition operators between Bloch-type and weighted-type spaces, providing new criteria and estimates for their essential norms.

Contribution

It introduces new equivalent characterizations for these operators' boundedness and compactness, and estimates their essential norms based on induced self-maps.

Findings

New criteria for boundedness and compactness

Essential norm estimates in terms of induced maps

Characterizations specific to differences of operators

Abstract

We found several new equivalent characterizations for the boundedness and compactness of the differences of weighted differentiation composition operators from Bloch-type space to weighted-type space. Especially, we estimated its essential norm in terms of the $n$-th power of the induced analytic self-maps on the unit disk.