Bergman空间上一类斜Toeplitz算子的交换性

Commutativity of a Class of Slant Toeplitz Operators on the Bergman Space

摘要: 本文主要研究单位圆盘的Bergman空间上斜Toeplitz算子的交换性问题，利用Mellin变换得到以径向函数为符号的斜Toeplitz算子与解析斜Toeplitz算子可交换的一个必要条件，以及以特殊径向函数为符号的斜Toeplitz算子与解析斜Toeplitz算子可交换的充要条件；并得到以函数$a{z}^s+b{\left|z\right|}^{2t}$ 为符号的斜Toeplitz算子与解析斜Toeplitz算子可交换的充要条件。

Abstract: In this paper, we primarily investigate the commutativity of the slant Toeplitz operator on the Bergman space of the unit disk. Using the Mellin transform, we obtain one necessary condition and some sufficient and necessary conditions for slant Toeplitz operators with radial symbols that commute with slant Toeplitz operators with analytic symbols, and the sufficient and necessary conditions for the commutativity of slant Toeplitz operators with function $a{z}^s+b{\left|z\right|}^{2t}$ and slant Toeplitz operators with analytic symbols.