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

摘要

On the weakly pseudo-convex domains $\Omega_p^n$ we introducequasi-homogeneous quasi-radial symbols. These are used to prove the existenceof a commutative Banach algebra of Toeplitz operators on Bergman space of$\Omega_p^n$. We also show that group theoretic and geometric properties forour symbols are satisfied. The results presented here contain the geometricdescription of the symbols introduced by N. Vasilevski for the unit ball$\mathbb{B}^n$.