Sharp Sobolev regularity of restricted X-ray transforms
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866929596590456832 |
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| author | Ko, Hyerim Lee, Sanghyuk Oh, Sewook |
| author_facet | Ko, Hyerim Lee, Sanghyuk Oh, Sewook |
| contents | We study $L^p$-Sobolev regularity estimate for the restricted X-ray transforms generated by nondegenerate curves. Making use of the inductive strategy in the recent work by the authors, we establish the sharp $L^p$-regularity estimates for the restricted X-ray transforms in $\mathbb R^{d+1}$, $d\ge 3$. This extends the result due to Pramanik and Seeger in $\mathbb R^3$ to every dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_04339 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Sharp Sobolev regularity of restricted X-ray transforms Ko, Hyerim Lee, Sanghyuk Oh, Sewook Classical Analysis and ODEs Analysis of PDEs We study $L^p$-Sobolev regularity estimate for the restricted X-ray transforms generated by nondegenerate curves. Making use of the inductive strategy in the recent work by the authors, we establish the sharp $L^p$-regularity estimates for the restricted X-ray transforms in $\mathbb R^{d+1}$, $d\ge 3$. This extends the result due to Pramanik and Seeger in $\mathbb R^3$ to every dimension. |
| title | Sharp Sobolev regularity of restricted X-ray transforms |
| topic | Classical Analysis and ODEs Analysis of PDEs |
| url | https://arxiv.org/abs/2111.04339 |