加权Dirichlet空间上具有无界符号的Toeplitz算子(英文)

TOEPLITZ OPERATORS WITH UNBOUNDED SYMBOLS ON WEIGHTED DIRICHLET SPACE

本文研究了加权Dirichlet空间上一类Toeplitz性质的问题.利用构造单位圆盘D上一类无界函数的方法,获得了以它为符号的Toeplitz算子是紧的结果.同时也通过构造一类L2(?)上的函数,使得它们在单位圆周上每一点的任何一个邻域都无界的方法,获得了以这些函数为符号的Toeplitz算子是迹类算子的结果.

In this paper, we study the properties of a class of Toeplitz operators on weighted Dirichlet space. By using the method of constructing a class of unbounded function on D, we prove that the Toeplitz operators with these symbols are compact. Also by using the method of constructing a function Ф in L2φwhich is unbounded on any neighborhood of each boundary point of D, we prove that Tφis a trace class operator on weighted Dirichlet space.