Commutants of quasihomogeneous Toeplitz operators on the harmonic Bergman space

TL;DR

This paper investigates the structure of the commutant of quasihomogeneous Toeplitz operators on the harmonic Bergman space, aiming to characterize all operators that commute with a given class of these Toeplitz operators.

Contribution

It provides a detailed description of the commutants of quasihomogeneous Toeplitz operators on the harmonic Bergman space, extending understanding of their algebraic properties.

Findings

Characterization of commutants for a class of quasihomogeneous Toeplitz operators

Identification of conditions under which Toeplitz operators commute

Extension of known results to harmonic Bergman space context

Abstract

One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk $\mathbb{D}$ in the complex place $\mathbb{C}$ is to completely describe the commutant of a given Toeplitz operator, that is, the set of all Toeplitz operators that commute with it. Here we shall study the commutants of a certain class of quasihomogeneous Toeplitz operators.