Sharp Fourier extension on fractional surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929404730408960 |
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| author | Di, Boning Yan, Dunyan |
| author_facet | Di, Boning Yan, Dunyan |
| contents | For $α\geq 2$, we investigate a class of Fourier extension operators on fractional surfaces $(ξ,|ξ|^α)$. For the corresponding $α$-Strichartz inequalities, by applying the missing mass method and bilinear restriction theory, we characterize the precompactness of extremal sequences. Our result is valid in any dimension. In particular for dimension two, our result implies the existence of extremals for $α\in [2,α_0)$ with some $α_0>5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_06981 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sharp Fourier extension on fractional surfaces Di, Boning Yan, Dunyan Classical Analysis and ODEs Analysis of PDEs Functional Analysis 42B10 (Primary), 42B37, 35B38, 35Q41 (Secondary) For $α\geq 2$, we investigate a class of Fourier extension operators on fractional surfaces $(ξ,|ξ|^α)$. For the corresponding $α$-Strichartz inequalities, by applying the missing mass method and bilinear restriction theory, we characterize the precompactness of extremal sequences. Our result is valid in any dimension. In particular for dimension two, our result implies the existence of extremals for $α\in [2,α_0)$ with some $α_0>5$. |
| title | Sharp Fourier extension on fractional surfaces |
| topic | Classical Analysis and ODEs Analysis of PDEs Functional Analysis 42B10 (Primary), 42B37, 35B38, 35Q41 (Secondary) |
| url | https://arxiv.org/abs/2209.06981 |