Commuting Dual Toeplitz Operators on the Harmonic Dirichlet Space

被引：5

作者：

Yang, Jing Yu ^{[1
]}

Hu, Yin Yin ^{[2
]}

Lu, Yu Feng ^{[2
]}

Yu, Tao ^{[2
]}

机构：

[1] Chifeng Univ, Sch Math Stat, Chifeng 024000, Peoples R China

[2] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2016年 / 32卷 / 09期

关键词：

Dual Toeplitz operator; harmonic Dirichlet space; commutativity; PLURIHARMONIC SYMBOLS; ORTHOGONAL COMPLEMENT; ALGEBRAIC PROPERTIES; BERGMAN SPACES; COMMUTANTS;

D O I：

10.1007/s10114-016-5663-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we characterize the symbols for (semi-)commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for phi, psi is an element of W (1,infinity), S phi S psi = S psi S phi on (D-h )(perpendicular to) if and only if phi and psi satisfy one of the following conditions: (1) Both phi and psi are harmonic functions; (2) There exist complex constants alpha and beta, not both 0, such that phi = alpha psi+beta.

引用

页码：1099 / 1105

页数：7

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