On the boundedness of Dunkl multipliers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910852548919296 |
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| author | Mukherjee, Suman Thangavelu, Sundaram |
| author_facet | Mukherjee, Suman Thangavelu, Sundaram |
| contents | In this article we use Littlewood-Paley-Stein theory to prove two versions of Dunkl multiplier theorem when the multiplier $ m $ satisfies a modified Hörmander condition. When $ m $ is radial we give a simple proof of a known result. For general $ m $ we prove that the Dunkl multiplier operator takes radial functions in $ L^p $ boundedly into $ L^p $ for all $ p \geq 2.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16731 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the boundedness of Dunkl multipliers Mukherjee, Suman Thangavelu, Sundaram Functional Analysis Classical Analysis and ODEs 42B15, 42B25, 47G10, 47B34 In this article we use Littlewood-Paley-Stein theory to prove two versions of Dunkl multiplier theorem when the multiplier $ m $ satisfies a modified Hörmander condition. When $ m $ is radial we give a simple proof of a known result. For general $ m $ we prove that the Dunkl multiplier operator takes radial functions in $ L^p $ boundedly into $ L^p $ for all $ p \geq 2.$ |
| title | On the boundedness of Dunkl multipliers |
| topic | Functional Analysis Classical Analysis and ODEs 42B15, 42B25, 47G10, 47B34 |
| url | https://arxiv.org/abs/2406.16731 |