A Kakeya maximal estimate for regulus strips
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866912108470337536 |
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| author | Wu, Shukun |
| author_facet | Wu, Shukun |
| contents | We prove Kakeya-type estimates for regulus strips. As a result, we obtain another epsilon improvement over the Kakeya conjecture in $\mathbb{R}^3$, by showing that the regulus strips in the ${\rm SL}_2$ example are essentially disjoint. We also establish an $L^p$ inequality regarding Nikodym-type maximal function in the first Heisenberg group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04438 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Kakeya maximal estimate for regulus strips Wu, Shukun Classical Analysis and ODEs We prove Kakeya-type estimates for regulus strips. As a result, we obtain another epsilon improvement over the Kakeya conjecture in $\mathbb{R}^3$, by showing that the regulus strips in the ${\rm SL}_2$ example are essentially disjoint. We also establish an $L^p$ inequality regarding Nikodym-type maximal function in the first Heisenberg group. |
| title | A Kakeya maximal estimate for regulus strips |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2411.04438 |