单位球Dirichlet空间上的紧Toeplitz算子

Compact Toeplitz operators on the Dirichlet space over unit ball

研究单位球上Dirichlet空间上的Toeplitz算子的紧性,得到结论:有限个具有有界符号的Toeplitz算子乘积的有限和是一个紧算子,等价于它的Berezin型变换消失于单位球面。

The compactness of Toeplitz operators on Dirichlet space is studied.It is proved that finite sums of finite products of Toeplitz operators with bounded symbols are compact if and only if their Berez-in-type transforms vanish on the boundary of the unit ball.