加权调和Dirichlet空间上的紧Toeplitz算子

Compact Toeplitz operators on weighted harmonic Dirichlet space

考虑了加权调和Dirichlet空间上有限个Toeplitz算子乘积的有限和,得出其为紧算子的充要条件:当z趋于单位圆盘边界时,其Berezin变换趋于0.

The compact of Toeplitz operator on function spaces has been concerned. And in this paper we investigate a finite sum of finite products of Toeplitz operator on weighted harmonic Dirichlet space of unit disk, an equivalence condition of compactness of it is when z→δD , its Berezin type transform tends to 0.