A sharp weighted Fourier extension estimate for the cone in $\mathbb{R}^3$ based on circle tangencies
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909837960413184 |
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| author | Ortiz, Alexander |
| author_facet | Ortiz, Alexander |
| contents | We apply recent circle tangency estimates due to Pramanik--Yang--Zahl to prove sharp weighted Fourier extension estimates for the cone in $\mathbb{R}^3$ and $1$-dimensional weights. The idea of using circle tangency estimates to study Fourier extension of the cone is originally due to Tom Wolff, who used it in part to prove the first decoupling estimates. We make an improvement to the best known Mizohata--Takeuchi-type estimates for the cone in $\mathbb{R}^3$ and the $1$-dimensional weights as a corollary of our main theorem, where the previously best known bound follows as a corollary of refined decoupling estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11731 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A sharp weighted Fourier extension estimate for the cone in $\mathbb{R}^3$ based on circle tangencies Ortiz, Alexander Classical Analysis and ODEs 42B10 We apply recent circle tangency estimates due to Pramanik--Yang--Zahl to prove sharp weighted Fourier extension estimates for the cone in $\mathbb{R}^3$ and $1$-dimensional weights. The idea of using circle tangency estimates to study Fourier extension of the cone is originally due to Tom Wolff, who used it in part to prove the first decoupling estimates. We make an improvement to the best known Mizohata--Takeuchi-type estimates for the cone in $\mathbb{R}^3$ and the $1$-dimensional weights as a corollary of our main theorem, where the previously best known bound follows as a corollary of refined decoupling estimates. |
| title | A sharp weighted Fourier extension estimate for the cone in $\mathbb{R}^3$ based on circle tangencies |
| topic | Classical Analysis and ODEs 42B10 |
| url | https://arxiv.org/abs/2307.11731 |