The Commutants Of The Toeplitz Operators With Radial Symbols On The Pluriharmonic Bergman Space

Toeplitz operator on Bergman space is an active branch in operator theory. They are not only closely related with the other discipline of mathematics, but also have many im-portant applications in quantummechanics, probability and statistics, control, etc. Since the last century fifties, the study of Toeplitz operator has a good development, especially on the Bergman space, and many results have been obtained. On the Bergman space, Toeplitz operators with harmonic symbols is well studied, but Toeplitz operators with general symbols seems quite challenging and is not fully understand now. In this pa-per, we characterize the commutants of the Toeplitz operator with radial symbols on the pluriharmonic Bergman space on the unit ball. The main contents of this paper is as follows:In chapter1, some background information about Toeplitz operators is reviewed.In chapter2, we introduce some basic concepts and properties of Bergman spaces and Toeplitz operators on it.In chapter3, we introduce some basic concepts and properties of radial functions and quasihomogeneous functions on Bergman space and the Mellin transform.In chapter4, we characterize the commutants of the Toeplitz operator with radial symbols on the pluriharmonic Bergman space on the unit ball.