Weighted Composition Operators from Hardy to Zygmund Type Spaces

Abstract

This paper aims at studying the boundedness and compactness of weighted composition operator between spaces of analytic functions. We characterize boundedness and compactness of the weighted composition operator $u{C}_{\varphi }$ from the Hardy spaces $H^p$ to the Zygmund type spaces and the little Zygmund type spaces ${𝒵}_{\alpha ,0}$ in terms of function theoretic properties of the symbols $u$ and $\varphi$.