Toeplitz Operators with Quasi-Homogeneuos Quasi-Radial Symbols on Some Weakly Pseudoconvex Domains

On the weakly pseudo-convex domains Ωpn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _p^n$$\end{document} we introduce quasi-homogeneous quasi-radial symbols. These are used to prove the existence of a commutative Banach algebra of Toeplitz operators on Bergman space of Ωpn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _p^n$$\end{document}. We also show that group theoretic and geometric properties for our symbols are satisfied. The results presented here contain the geometric description of the symbols introduced by  Vasilevski in (Integr Equ Operat Theory, 66(1):141–152, 2010) for the unit ball Bn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {B}^n$$\end{document}.