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

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.