单位球上多重调和Bergman空间上的k-拟齐次Toeplitz算子

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

摘要:

本文研究了单位球上多重调和 Bergman 空间上 k-拟齐次 Toeplitz 算子的基本性质，得到了其上两个该类算子所构成的交换子和半交换子的对称性质. 此外, 本文还得到了其上两个单项式形 Toeplitz 算子构成的交换子和半交换子有有限秩的充分必要条件.

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.