多圆盘上的本质可换的Toeplitz算子

On Essentially Commuting Toeplitz Operators on the Polydisk

本文讨论多圆盘上Ｂｅｒｇｍａｎ空间上的具有多重调和符号的Ｔｏｅｐｌｉｔｚ算子的本质可换性与可换性．我们获得了一个解析或共轭解析Ｔｏｅｐｌｉｔｚ算子与具有多重调和符号的Ｔｏｅｐｌｉｔｚ算子本质可换的充分必要条件是它们是可换的．

In this paper, we characterize commuting and essentially commuting Toeplitz operators with bounded pluriharmophic symbols on Bergman space of the polydisk D^n for n > 1. A analytic Toeplitz operator and pluriharmophic Toeplitz operator essentially commute if and only if they commute.