Weighted Composition Operators Between Zygmund Type Spaces and Their Essential Norms

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${u \in \mathcal{H}(\mathbb{D})}$$\end{document} and φ be an analytic self-map of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{D}}$$\end{document}. 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.