End-point estimates of the totally-geodesic Radon transform on simply connected spaces of constant curvature: A Unified Approach
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918104460689408 |
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| author | Deshmukh, Aniruddha Kumar, Ashisha |
| author_facet | Deshmukh, Aniruddha Kumar, Ashisha |
| contents | In this article, we give a unified proof of the end-point estimates of the totally-geodesic $k$-plane transform of radial functions on spaces of constant curvature. The problem of getting end-point estimates is not new and some results are available in literature. However, these results were obtained independently without much focus on the similarities between underlying geometries. We give a unified proof for the end-point estimates on spaces of constant curvature by making use of geometric ideas common to the spaces of constant curvature, and obtaining a unified formula for the $k$-plane transform of radial functions. We also give some inequalities for certain special functions as an application to one of our lemmata. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_13541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | End-point estimates of the totally-geodesic Radon transform on simply connected spaces of constant curvature: A Unified Approach Deshmukh, Aniruddha Kumar, Ashisha Functional Analysis Differential Geometry 44A12, 47A30, 43A85, 46E30 In this article, we give a unified proof of the end-point estimates of the totally-geodesic $k$-plane transform of radial functions on spaces of constant curvature. The problem of getting end-point estimates is not new and some results are available in literature. However, these results were obtained independently without much focus on the similarities between underlying geometries. We give a unified proof for the end-point estimates on spaces of constant curvature by making use of geometric ideas common to the spaces of constant curvature, and obtaining a unified formula for the $k$-plane transform of radial functions. We also give some inequalities for certain special functions as an application to one of our lemmata. |
| title | End-point estimates of the totally-geodesic Radon transform on simply connected spaces of constant curvature: A Unified Approach |
| topic | Functional Analysis Differential Geometry 44A12, 47A30, 43A85, 46E30 |
| url | https://arxiv.org/abs/2408.13541 |