A convolution type characterization for Lp - multipliers for the Heisenberg group
It is well known that if m is an Lp - multiplier for the Fourier transform on ℝn(1<p<∞) , then there exists a pseudomeasure σ such that Tmf =σ*f. A similar result is proved for the group Fourier transform on the Heisenberg group Hn. Though this result is already known in generality for a...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2007/701403 |
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| _version_ | 1832545446243860480 |
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| author | R. Radha A.K. Vijayarajan |
| author_facet | R. Radha A.K. Vijayarajan |
| author_sort | R. Radha |
| collection | DOAJ |
| description | It is well known that if m is an Lp - multiplier for the Fourier transform on ℝn(1<p<∞) , then there exists a pseudomeasure σ such that Tmf =σ*f. A similar result is proved for the group Fourier transform on the Heisenberg group Hn. Though this result is already known in generality for amenable groups, a simple proof is provided in this paper. |
| format | Article |
| id | doaj-art-7826df4127504a0896ab9fb9bafcdda1 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-7826df4127504a0896ab9fb9bafcdda12025-02-03T07:25:48ZengWileyJournal of Function Spaces and Applications0972-68022007-01-015217518210.1155/2007/701403A convolution type characterization for Lp - multipliers for the Heisenberg groupR. Radha0A.K. Vijayarajan1Department of Mathematics, Indian Institute of Technology Madras, Chennai - 600 036, IndiaSchool of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UKIt is well known that if m is an Lp - multiplier for the Fourier transform on ℝn(1<p<∞) , then there exists a pseudomeasure σ such that Tmf =σ*f. A similar result is proved for the group Fourier transform on the Heisenberg group Hn. Though this result is already known in generality for amenable groups, a simple proof is provided in this paper.http://dx.doi.org/10.1155/2007/701403 |
| spellingShingle | R. Radha A.K. Vijayarajan A convolution type characterization for Lp - multipliers for the Heisenberg group Journal of Function Spaces and Applications |
| title | A convolution type characterization for Lp - multipliers for the Heisenberg group |
| title_full | A convolution type characterization for Lp - multipliers for the Heisenberg group |
| title_fullStr | A convolution type characterization for Lp - multipliers for the Heisenberg group |
| title_full_unstemmed | A convolution type characterization for Lp - multipliers for the Heisenberg group |
| title_short | A convolution type characterization for Lp - multipliers for the Heisenberg group |
| title_sort | convolution type characterization for lp multipliers for the heisenberg group |
| url | http://dx.doi.org/10.1155/2007/701403 |
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