Differences of Composition Operators from Classical Zygmund Space to Bloch-type Space

Abstract

The aim of this paper is to explore the equivalent characterizations for the boundedness and compactness of C_φ − C_ψ acting from classical (little) Zygmund space \({\cal{Z}}({\cal{Z}}_{0})\) to (little) Bloch-type space \({\cal{B}}^{\alpha}\;({\cal{B}}_{0}^{\alpha})\). Especially, we creatively develop a useful lemma, which not only plays a crucial role in the estimations but also offers a sufficient condition for the bounded below property of composition operators.