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.

9 pages