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 : 𝔍 z > 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.