Weighted Fourier inequalities and application of restriction theorems on rank one Riemannian symmetric spaces of noncompact type
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913383943503872 |
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| author | Kumar, Pratyoosh Pusti, Sanjoy Rana, Tapendu Singh, Mandeep |
| author_facet | Kumar, Pratyoosh Pusti, Sanjoy Rana, Tapendu Singh, Mandeep |
| contents | This article explores weighted $(L^p, L^q)$ inequalities for the Fourier transform in rank one Riemannian symmetric spaces of noncompact type. We establish both necessary and sufficient conditions for these inequalities to hold. To prove the weighted Fourier inequalities, we apply restriction theorems on symmetric spaces and utilize Calder{ó}n's estimate for sublinear operators. While establishing the necessary conditions, we demonstrate that Harish-Chandra's elementary spherical functions play a crucial role in this setting. Furthermore, we apply our findings to derive Fourier inequalities with polynomial and exponential weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06268 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted Fourier inequalities and application of restriction theorems on rank one Riemannian symmetric spaces of noncompact type Kumar, Pratyoosh Pusti, Sanjoy Rana, Tapendu Singh, Mandeep Classical Analysis and ODEs Functional Analysis Primary 43A85, 43A90, Secondary 22E30 This article explores weighted $(L^p, L^q)$ inequalities for the Fourier transform in rank one Riemannian symmetric spaces of noncompact type. We establish both necessary and sufficient conditions for these inequalities to hold. To prove the weighted Fourier inequalities, we apply restriction theorems on symmetric spaces and utilize Calder{ó}n's estimate for sublinear operators. While establishing the necessary conditions, we demonstrate that Harish-Chandra's elementary spherical functions play a crucial role in this setting. Furthermore, we apply our findings to derive Fourier inequalities with polynomial and exponential weights. |
| title | Weighted Fourier inequalities and application of restriction theorems on rank one Riemannian symmetric spaces of noncompact type |
| topic | Classical Analysis and ODEs Functional Analysis Primary 43A85, 43A90, Secondary 22E30 |
| url | https://arxiv.org/abs/2406.06268 |