Compact Differences of Weighted Composition Operators

Abstract

Compact differences of two weighted composition operators acting from the weighted Bergman space $A_{\omega }^p$ to another weighted Bergman space $A_{\nu }^q$, where $0<p\le q<\infty$ and $\omega ,\nu$ belong to the class $\mathcal{D}$ of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proof a new description of $q$-Carleson measures for $A_{\omega }^p$, with $\omega \in \mathcal{D}$, in terms of pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of $q$-Carleson measures for the classical weighted Bergman space $A_{\alpha }^p$ with $-1<\alpha <\infty$ to the setting of doubling weights.

14 pages

References in corpus (1)

• Embedding theorems for Bergman spaces via harmonic analysis

Cited by in corpus (1)

• Generalized weighted composition operators on Bergman spaces induced by doubling weights