| 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(φ)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. |
| 关键词: 加权Dirichlit空间 无界符号 迹类算子 Toeplitz算子 |
| DOI： |
| 分类号:O177.1 |
| 基金项目:Supported by National Natural Science Foundation of China(10971040). |
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| TOEPLITZ OPERATORS WITH UNBOUNDEDSYMBOLS ON WEIGHTED DIRICHLET SPACE |
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HE Zhong-hua1, HE Li2, CAO Guang-fu3
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1.Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China;2.School of Math. and Computational Science, Sun Yat-Sen University, Guangzhou 510275, China;3.School of Math. and Information Science, Guangzhou University, Guangzhou 510006, China
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| Abstract: |
| 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 φ in Lφ2 which is unbounded on any neighborhood of each boundary point of D, we prove that Tφ is a trace class operator on weighted Dirichlet space. |
| Key words: weighted Dirchlet space unbounded symbol trace class operator Toeplitz operator |
