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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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/1054768 |
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| _version_ | 1849692562346999808 |
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| author | Yinyin Hu Yufeng Lu Tao Yu |
| author_facet | Yinyin Hu Yufeng Lu Tao Yu |
| author_sort | Yinyin Hu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-ea2a1a7b15c945009d45c47565afac5b |
| institution | DOAJ |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-ea2a1a7b15c945009d45c47565afac5b2025-08-20T03:20:39ZengWileyJournal 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2016/1054768 |
| work_keys_str_mv | AT yinyinhu propertiesofcommutativityofdualtoeplitzoperatorsontheorthogonalcomplementofpluriharmonicdirichletspaceovertheball AT yufenglu propertiesofcommutativityofdualtoeplitzoperatorsontheorthogonalcomplementofpluriharmonicdirichletspaceovertheball AT taoyu propertiesofcommutativityofdualtoeplitzoperatorsontheorthogonalcomplementofpluriharmonicdirichletspaceovertheball |