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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.22695 |
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| _version_ | 1866914213355585536 |
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| author | Ham, Seheon Ko, Hyerim |
| author_facet | Ham, Seheon Ko, Hyerim |
| contents | In this paper, we obtain local smoothing estimates for the averages over nondegenerate surfaces of codimension $2$ in $\mathbb R^4$. We make use of multilinear restriction estimates and decoupling inequalities for a hypersurface in $\mathbb R^5$, a conical extension of a two-dimensional nondegenerate surface along two flat directions. We also establish sharp $L^p$--$L^q$ estimates for maximal averages over nondegenerate surfaces of half the ambient dimension in $\mathbb R^{2n}$ for even $n \ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local smoothing and maximal estimates for average over surfaces of codimension 2 in $\mathbb R^4$ Ham, Seheon Ko, Hyerim Classical Analysis and ODEs 42B25 In this paper, we obtain local smoothing estimates for the averages over nondegenerate surfaces of codimension $2$ in $\mathbb R^4$. We make use of multilinear restriction estimates and decoupling inequalities for a hypersurface in $\mathbb R^5$, a conical extension of a two-dimensional nondegenerate surface along two flat directions. We also establish sharp $L^p$--$L^q$ estimates for maximal averages over nondegenerate surfaces of half the ambient dimension in $\mathbb R^{2n}$ for even $n \ge 2$. |
| title | Local smoothing and maximal estimates for average over surfaces of codimension 2 in $\mathbb R^4$ |
| topic | Classical Analysis and ODEs 42B25 |
| url | https://arxiv.org/abs/2507.22695 |