Composition operators from weighted Bergman spaces to some spaces of analytic functions on the upper half-plane

Abstract

Let Π+ = {z ∈ C : Imz > 0} be the upper halfplane in the complex plane C. Motivated by some recent results by Stevič, this paper characterizes the bounded composition operator from the weighted Bergman space A^p_α(Π⁺), 1 ≤ p < ∞, α ≥ 0, to the Zygmund-type space the weighted-type space .A∞ (Π⁺) and the Bloch-type space B∞ (Π⁺).