Weighted Composition Operators between Different Hardy Spaces

Abstract

Let \( \varphi \) and \( \psi \) be two analytic functions defined on \( \mathbb{D} \) such that\( \varphi(\mathbb{D}) \subseteq\mathbb{D} \). The operator given by \( f\mapsto\psi(f\circ\varphi) \) is called a weighted composition operator. In this paper we deal with the boundedness, compactness, weak compactness, and complete continuity of weighted composition operators from a Hardy space Hp into another Hardy space Hq\( ($1\leq p, q\leq\infty$) \). We apply these results to study composition operators on Hardy spaces of a half-plane.