2-Complex Symmetric Weighted Composition Operators on the Weighted Bergman Spaces of the Half-Plane

In the paper, 2-complex symmetric weighted composition operators induced by three type symbols on the weighted Bergman spaces of the right half-plane with three conjugations Jf(z)=f(z¯)¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Jf(z)=\overline{f(\bar{z})}$$\end{document}, Jsf(z)=f(z¯+is)¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_sf(z)=\overline{f(\bar{z}+is)}$$\end{document} and J∗f(z)=1zα+2f(1z¯)¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_*f(z)=\frac{1}{z^{\alpha +2}}\overline{f(\frac{1}{\bar{z}})}$$\end{document} are characterized by building the relations between some parameters. Some examples of such operators are also given.