Dirichlet空间上的Toeplitz算子

J4 ›› 2010, Vol. 48 ›› Issue (1): 33-38.

Dirichlet空间上的Toeplitz算子

邓燕¹, 陈泳^2,3

1. 嘉兴学院数学与信息工程学院, 浙江嘉兴 314001;2. 浙江师范大学数理与信息工程学院, 浙江金华 321004;3. 复旦大学数学科学学院, 上海 200433

收稿日期:2009-03-23 出版日期:2010-01-26 发布日期:2010-01-27
通讯作者: 邓燕 E-mail:dengyan878@163.com.

Toeplitz Operator on the Dirichlet Space

DENG Yan¹, CHEN Yong^2,3

1. College of Mathematics and Information Engineering, Jiaxing University, Jiaxing 314001, Zhejiang Province, China;2. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua |321004,Zhejiang Province, China|
3. School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received:2009-03-23 Online:2010-01-26 Published:2010-01-27
Contact: DENG Yan E-mail:dengyan878@163.com.

摘要/Abstract

摘要：

在经典导数意义下, 利用积分直接定义Dirichlet空间上的Toeplitz算子, 并引入一类连续符号, 研究Dirichlet空间上此类符号的Toeplitz算子
的一些基本性质, 得到了Toeplitz算子有限秩和零积问题的充分条件.

关键词: Toeplitz算子； Dirichlet空间；拟齐次符号；有限秩；零积

Abstract:

Under the classical differential sense, the Toeplitz operator with general symbol on the Dirichlet space is defined by directly using integral. And a class of continuous symbols is introduced. Toeplitz operators on the Dirichlet space with these symbols are considered, obtaining the sufficient conditions for finite rank Toeplitz operators and zero product pro
blems on the Dirichlet space.

Key words: Toeplitz operator, Dirichlet space, quasihomogeneous symbols, finite rank, zero product

中图分类号:

O177.6

邓燕, 陈泳. Dirichlet空间上的Toeplitz算子[J]. J4, 2010, 48(1): 33-38.

DENG Yan, CHEN Yong. Toeplitz Operator on the Dirichlet Space[J]. J4, 2010, 48(1): 33-38.