k-quasi-homogeneous Toeplitz operators on pluriharmonic Bergman space of the unit ball

Abstract:

In this paper, we study some basic properties of k-quasi-homogeneous Toeplitz operators on the pluriharmonic Bergman space of the unit ball, and obtain the symmetric properties of the commutator and semi-commutator consisting of two such operators. In addition, we obtain the sufficient and necessary conditions for the finite rank of commutator and semi-commutator of two monomial-type Toeplitz operators.

Key words:Toeplitz operator; Pluriharmonic Bergman space; k-quasi-homogeneous function