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

Abstract

Let ψ be a holomorphic mapping on the upper half-plane Π+={z∈ℂ:Jz>0} and φ be a holomorphic self-map of Π+. 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 ψ, we also characterize the compactness of these operators.