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

TL;DR

This paper introduces quasi-homogeneous quasi-radial symbols on weakly pseudoconvex domains, demonstrating their role in forming a commutative Banach algebra of Toeplitz operators and extending geometric descriptions from the unit ball.

Contribution

It develops a new class of symbols on complex domains and proves their associated Toeplitz operators form a commutative algebra, generalizing previous geometric results.

Findings

Existence of a commutative Banach algebra of Toeplitz operators.

Group theoretic and geometric properties of the symbols.

Extension of geometric descriptions to weakly pseudoconvex domains.

Abstract

On the weakly pseudo-convex domains $\Omega_p^n$ 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 $\Omega_p^n$. 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 $\mathbb{B}^n$.