Commuting dual Toeplitz operators on the orthogonal complement of the Dirichlet space

被引：22
作者：
Yu, Tao [1 ]
Wu, Shi Yue [1 ]
机构：
[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2009年 / 25卷 / 02期
关键词：
Sobolev space; Dirichlet space; dual Toeplitz operator;
D O I：
10.1007/s10114-008-7109-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator.
引用
收藏
页码：245 / 252
页数：8
相关论文
共 13 条
[1]  
Adams R., 2003, Pure and Applied Mathematics, V140
[2]   COMMUTING TOEPLITZ-OPERATORS WITH HARMONIC SYMBOLS [J].
AXLER, S ;
CUCKOVIC, Z .
INTEGRAL EQUATIONS AND OPERATOR THEORY, 1991, 14 (01) :1-12
[3]  
Brown A., 1964, J. Reine. Angew. Math, V213, P89
[4]   Fredholm properties of Toeplitz operators on Dirichlet spaces [J].
Cao, GF .
PACIFIC JOURNAL OF MATHEMATICS, 1999, 188 (02) :209-223
[5]  
CHENG G, CHIN Q J MA IN PRESS
[6]   Toeplitz operators on the Dirichlet space [J].
Duistermaat, JJ ;
Lee, YJ .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 300 (01) :54-67
[7]   Algebraic properties of Toeplitz operators on the Dirichlet space [J].
Lee, Young Joo .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 329 (02) :1316-1329
[8]   Commuting dual Toeplitz operators with pluriharmonic symbols [J].
Lu, WF .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 302 (01) :149-156
[9]   Commuting dual Toeplitz operators on the polydisk [J].
Lu, Yu Feng ;
Shang, Shu Xia .
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2007, 23 (05) :857-868
[10]   Algebraic and spectral properties of dual Toeplitz operators [J].
Stroethoff, K ;
Zheng, DC .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 354 (06) :2495-2520
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