Essential norms of weighted composition operators between Lipschitz spaces of arbitrary order

TL;DR

This paper characterizes the boundedness and estimates the essential norms of weighted composition operators acting between Lipschitz spaces of arbitrary order on the unit disk, extending the understanding of operator behavior in complex analysis.

Contribution

It provides a comprehensive characterization and norm estimates for weighted composition operators between Lipschitz spaces of any real order, generalizing previous results.

Findings

Characterization of bounded weighted composition operators between Lipschitz spaces.

Estimates for the essential norms of these operators.

Extension of results to all real orders of Lipschitz spaces.

Abstract

Let $\mathbb{D}$ denote the unit disk of $\mathbb{C}$ and let $\Lambda^\alpha(\mathbb{D})$ denote the scale of holomorphic Lipschitz spaces extended to all $\alpha\in\mathbb{R}$. For arbitrary $\alpha, \beta\in\mathbb{R}$, we characterize the bounded weighted composition operators from $\Lambda^\beta(\mathbb{D})$ into $\Lambda^\alpha(\mathbb{D})$ and estimate their essential norms.