Asymptotics and Isometries of Weighted Composition Operators on Banach Spaces of Holomorphic Functions

We have developed some convergence criteria for the weighted composition operators on various Banach spaces of holomorphic functions, which also extends some of the results of Chalendar and Partington (Weighted Composition Operators: Isometries and Asymptotic Behaviour, 2019). We have also characterized the isometries of the weighted composition operators on the Hardy spaces Hp(D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^p({\mathbb {D}})$$\end{document}, which extends the characterization of the isometric weighted composition operators on the Hardy-Hilbert space H2(D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^2({\mathbb {D}})$$\end{document} done in Kumar and Partington (Oper Theory Adv Appl 153:157–167).