Weighted composition operators between growth spaces of the upper half-plane

Abstract

Let ψ be a holomorphic map of the upper half-plane Π⁺ and φ be a holomorphic self-map of Π⁺. We characterize bounded weighted composition operators acting between growth spaces of the upper half-plane. Under some conditions on φ and ψ, we also characterize compact weighted composition operators between growth spaces of the upper half-plane.