Weighted Composition Operators from Weighted Bergman Spaces to Weighted-Type Spaces on the Upper Half-Plane

Abstract

Let $\psi$ be a holomorphic mapping on the upper half-plane ${\Pi }^{+}=\{z\in ℂ:𝔍z>0\}$ and $\varphi$ be a holomorphic self-map of ${\Pi }^{+}$. We characterize bounded weighted composition operators acting from the weighted Bergman space to the weighted-type space on the upper half-plane. Under a mild condition on $\psi$, we also characterize the compactness of these operators.