Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball

Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball

We completely characterize the pluriharmonic symbols for (semi)commuting dual Toeplitz operators on the orthogonal complement of the pluriharmonic Dirichlet space in Sobolev space of the unit ball. We show that, for f and g pluriharmonic functions, SfSg=SgSf on (Dh)⊥ if and only if f and g satisfy o...

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Main Authors: Yinyin Hu, Yufeng Lu, Tao Yu
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2016/1054768
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spelling doaj-ea2a1a7b15c945009d45c47565afac5b2020-11-24T21:32:59ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/10547681054768Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the BallYinyin Hu0Yufeng Lu1Tao Yu2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116024, ChinaWe completely characterize the pluriharmonic symbols for (semi)commuting dual Toeplitz operators on the orthogonal complement of the pluriharmonic Dirichlet space in Sobolev space of the unit ball. We show that, for f and g pluriharmonic functions, SfSg=SgSf on (Dh)⊥ if and only if f and g satisfy one of the following conditions: (1) both f and g are holomorphic; (2) both f¯ and g¯ are holomorphic; (3) there are constants α and β, both not being zero, such that αf+βg is constant.http://dx.doi.org/10.1155/2016/1054768
collection DOAJ
language English
format Article
sources DOAJ
author Yinyin Hu
Yufeng Lu
Tao Yu
spellingShingle Yinyin Hu
Yufeng Lu
Tao Yu
Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball
Journal of Function Spaces
author_facet Yinyin Hu
Yufeng Lu
Tao Yu
author_sort Yinyin Hu
title Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball
title_short Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball
title_full Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball
title_fullStr Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball
title_full_unstemmed Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball
title_sort properties of commutativity of dual toeplitz operators on the orthogonal complement of pluriharmonic dirichlet space over the ball
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2016-01-01
description We completely characterize the pluriharmonic symbols for (semi)commuting dual Toeplitz operators on the orthogonal complement of the pluriharmonic Dirichlet space in Sobolev space of the unit ball. We show that, for f and g pluriharmonic functions, SfSg=SgSf on (Dh)⊥ if and only if f and g satisfy one of the following conditions: (1) both f and g are holomorphic; (2) both f¯ and g¯ are holomorphic; (3) there are constants α and β, both not being zero, such that αf+βg is constant.
url http://dx.doi.org/10.1155/2016/1054768
work_keys_str_mv AT yinyinhu propertiesofcommutativityofdualtoeplitzoperatorsontheorthogonalcomplementofpluriharmonicdirichletspaceovertheball
AT yufenglu propertiesofcommutativityofdualtoeplitzoperatorsontheorthogonalcomplementofpluriharmonicdirichletspaceovertheball
AT taoyu propertiesofcommutativityofdualtoeplitzoperatorsontheorthogonalcomplementofpluriharmonicdirichletspaceovertheball
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