A characterization of Zugmund-type spaces and its application

Abstract

In this paper, we investigate the conditions under which a Zygmund-type space Z_ω, where ω is a normal weight on the unit ball B^n of C^n, becomes a small space that is boundery regular and invariant under automorphisms. These results are then applied to analyze the relationship between the boundedness and compactness of weighted composition operators W_{ψ,φ}, defined by f →ψ·(f◦φ), acting from the Bloch-type space B_ω to the Zygmund-type space Z_ω, as well as from Z+ω to itself.