Difference of Composition Operators on Weighted Bergman Spaces with Doubling Weights

In this paper, some characterizations for the compact difference of composition operators on weighted Bergman spaces Aωp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A^p_\omega $$\end{document} with doubling weights are given, which extend Moorhouse’s characterization for the difference of composition operators on the weighted Bergman space Aα2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A^2_\alpha $$\end{document}.