Weighted Composition Operators on Iterated Weighted-Type Banach Spaces of Analytic Functions

Abstract

We study a class $$\{V_n : n\ge 0\}$$ of iterated weighted-type Banach spaces of analytic functions on the open unit disk of which the Bloch space and the Zygmund space are special cases. We characterize the bounded and the compact weighted composition operators on $$V_n$$ thereby extending several known results in the literature. Lastly, we characterize the invertible weighted composition operators on $$V_n$$ and prove that a composition operator on $$V_n$$ is an isometry if and only if its symbol is a rotation.