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

On the weakly pseudo-convex domains ${\mathrm{\Omega }}_p^n$ 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 ${\mathrm{\Omega }}_p^n$. 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 N. Vasilevski for the unit ball ${\mathbb{B}}^n$.