$l^2$ decoupling theorem for surfaces in $\mathbb{R}^3$
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911298165407744 |
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| author | Guth, Larry Maldague, Dominique Oh, Changkeun |
| author_facet | Guth, Larry Maldague, Dominique Oh, Changkeun |
| contents | We identify a new way to divide the $δ$-neighborhood of surfaces $\mathcal{M}\subset\mathbb{R}^3$ into a finitely-overlapping collection of rectangular boxes $S$. We obtain a sharp $(l^2,L^p)$ decoupling estimate using this decomposition, for the sharp range of exponents $2\leq p\leq 4$. Our decoupling inequality leads to new exponential sum estimates where the frequencies lie on surfaces which do not contain a line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18431 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $l^2$ decoupling theorem for surfaces in $\mathbb{R}^3$ Guth, Larry Maldague, Dominique Oh, Changkeun Classical Analysis and ODEs We identify a new way to divide the $δ$-neighborhood of surfaces $\mathcal{M}\subset\mathbb{R}^3$ into a finitely-overlapping collection of rectangular boxes $S$. We obtain a sharp $(l^2,L^p)$ decoupling estimate using this decomposition, for the sharp range of exponents $2\leq p\leq 4$. Our decoupling inequality leads to new exponential sum estimates where the frequencies lie on surfaces which do not contain a line. |
| title | $l^2$ decoupling theorem for surfaces in $\mathbb{R}^3$ |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2403.18431 |