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

作　　者：何忠华[1] 何莉[2] 曹广福[3] 

机构地区：[1]广东金融学院应用数学系,广东广州510521 [2]中山大学数学与计算科学学院,广东广州510275 [3]广州大学数学与信息科学学院,广东广州510006

出　　处：《数学杂志》2014年第3期461-468,共8页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(10971040)

摘　　要：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.

关 键 词：加权Dirichlit空间 无界符号 迹类算子 TOEPLITZ算子 

分 类 号：O177.1[理学—数学]