A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit Ball
This paper shows that if S is a bounded linear operator acting on the weighted Bergman spaces Aα2 on the unit ball in ℂn such that STzi=Tz¯iS (i=1,…,n), where Tzi=zif and Tz¯i=P(z¯if); and where P is the weighted Bergman projection, then S must be a Hankel operator.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2008/538573 |
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| _version_ | 1832548448086261760 |
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| author | Yufeng Lu Jun Yang |
| author_facet | Yufeng Lu Jun Yang |
| author_sort | Yufeng Lu |
| collection | DOAJ |
| description | This paper shows that if S is a bounded linear operator acting on the weighted Bergman spaces Aα2 on the unit ball in ℂn such that STzi=Tz¯iS (i=1,…,n), where Tzi=zif and Tz¯i=P(z¯if); and where P is the weighted Bergman projection, then S must be a Hankel operator. |
| format | Article |
| id | doaj-art-15fc286063a14b248a9ff5e805d30688 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-15fc286063a14b248a9ff5e805d306882025-02-03T06:14:05ZengWileyAbstract and Applied Analysis1085-33751687-04092008-01-01200810.1155/2008/538573538573A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit BallYufeng Lu0Jun Yang1Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, ChinaDepartment of Applied Mathematics, Dalian University of Technology, Dalian 116024, ChinaThis paper shows that if S is a bounded linear operator acting on the weighted Bergman spaces Aα2 on the unit ball in ℂn such that STzi=Tz¯iS (i=1,…,n), where Tzi=zif and Tz¯i=P(z¯if); and where P is the weighted Bergman projection, then S must be a Hankel operator.http://dx.doi.org/10.1155/2008/538573 |
| spellingShingle | Yufeng Lu Jun Yang A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit Ball Abstract and Applied Analysis |
| title | A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit Ball |
| title_full | A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit Ball |
| title_fullStr | A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit Ball |
| title_full_unstemmed | A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit Ball |
| title_short | A Theorem of Nehari Type on Weighted Bergman Spaces of the Unit Ball |
| title_sort | theorem of nehari type on weighted bergman spaces of the unit ball |
| url | http://dx.doi.org/10.1155/2008/538573 |
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