Weighted Composition Operators Between Zygmund Type Spaces and Their Essential Norms

Abstract

Let \({u \in \mathcal{H}(\mathbb{D})}\) and φ be an analytic self-map of \({\mathbb{D}}\). We estimate the essential norms of weighted composition operators uCφ acting on Zygmund type spaces in terms of u, φ, their derivatives and the n-th power φn of φ. Moreover, we give similar characterizations for boundedness of uCφ between Zygmund type spaces.