On the Commutativity of a Certain Class of Toeplitz Operators

Abstract

One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex place 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 defined on the harmonic Bergman space.

Toeplitz Operators with Radial Symbols on Bergman Space and Schatten-von Neumann Classes

“…We finish this subsection mentioning interesting related papers by Louhichi-Zakariasy [11], Louhichi-Strouse-Zakariasy [12], and Louhichi-Randrimahaleo-Zakariasy [13].…”