The Bedrosian Identity for Lp Function and the Hardy Space on Tube
In this paper, we are devoted to establishing several necessary and su cient conditions for <em>f</em>∈<em>L</em><sup><em>p</em></sup>(R<sup><em>n</em></sup>); <em>g</em>∈<em>L</em><sup><em>q&...
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| Language: | English |
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AIMS Press
2016-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://www.aimspress.com/article/10.3934/Math.2016.1.9/fulltext.html |
| _version_ | 1818343855781576704 |
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| author | Zhihong Wen Guantie Deng |
| author_facet | Zhihong Wen Guantie Deng |
| author_sort | Zhihong Wen |
| collection | DOAJ |
| description | In this paper, we are devoted to establishing several necessary and su cient conditions for <em>f</em>∈<em>L</em><sup><em>p</em></sup>(R<sup><em>n</em></sup>); <em>g</em>∈<em>L</em><sup><em>q</em></sup>(R<sup><em>n</em></sup>) with (1/<em>p</em>) +(1/<em>q</em>)≤1 to satisfy the Bedrosian identity <em>H</em>(<em>fg</em>) =<em>fHg</em>, where <em>H</em> denotes the n-dimensional Hilbert transform. In addition, we also show that the distribution <em>f</em>∈<em>DL</em><sup><em>p</em></sup>' (R<sup><em>n</em></sup>) can be represented by functions in the Hardy space on tube. |
| first_indexed | 2024-12-13T16:37:13Z |
| format | Article |
| id | doaj.art-9a858c9efb2b4b99b98345ffd8de5080 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-13T16:37:13Z |
| publishDate | 2016-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-9a858c9efb2b4b99b98345ffd8de50802022-12-21T23:38:22ZengAIMS PressAIMS Mathematics2473-69882016-04-011192310.3934/Math.2016.1.9The Bedrosian Identity for Lp Function and the Hardy Space on TubeZhihong Wen0Guantie Deng1School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems ofMinistry of Education, Beijing Normal University, 100875, Beijing, ChinaSchool of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems ofMinistry of Education, Beijing Normal University, 100875, Beijing, ChinaIn this paper, we are devoted to establishing several necessary and su cient conditions for <em>f</em>∈<em>L</em><sup><em>p</em></sup>(R<sup><em>n</em></sup>); <em>g</em>∈<em>L</em><sup><em>q</em></sup>(R<sup><em>n</em></sup>) with (1/<em>p</em>) +(1/<em>q</em>)≤1 to satisfy the Bedrosian identity <em>H</em>(<em>fg</em>) =<em>fHg</em>, where <em>H</em> denotes the n-dimensional Hilbert transform. In addition, we also show that the distribution <em>f</em>∈<em>DL</em><sup><em>p</em></sup>' (R<sup><em>n</em></sup>) can be represented by functions in the Hardy space on tube.http://www.aimspress.com/article/10.3934/Math.2016.1.9/fulltext.htmlBedrosian identity|Fourier transform|Hilbert transform|Distribution |
| spellingShingle | Zhihong Wen Guantie Deng The Bedrosian Identity for Lp Function and the Hardy Space on Tube AIMS Mathematics Bedrosian identity|Fourier transform|Hilbert transform|Distribution |
| title | The Bedrosian Identity for Lp Function and the Hardy Space on Tube |
| title_full | The Bedrosian Identity for Lp Function and the Hardy Space on Tube |
| title_fullStr | The Bedrosian Identity for Lp Function and the Hardy Space on Tube |
| title_full_unstemmed | The Bedrosian Identity for Lp Function and the Hardy Space on Tube |
| title_short | The Bedrosian Identity for Lp Function and the Hardy Space on Tube |
| title_sort | bedrosian identity for lp function and the hardy space on tube |
| topic | Bedrosian identity|Fourier transform|Hilbert transform|Distribution |
| url | http://www.aimspress.com/article/10.3934/Math.2016.1.9/fulltext.html |
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