On $L^p$ extremals for Fourier extension estimate to fractional surface
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909507165093888 |
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| author | Di, Boning Liu, Ning Yan, Dunyan |
| author_facet | Di, Boning Liu, Ning Yan, Dunyan |
| contents | This article investigates the Fourier extension operator associated with the fractional surface $(ξ,|ξ|^α)$ for $α\geq 2$. We show that the relevant $L^p\to L^q$ Fourier extension inequality possesses extremals for all exponents $p\in[1,2]$. Moreover, for all $p\in(1,2]$, the corresponding $L^p$-extremal sequences are precompact up to symmetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10693 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $L^p$ extremals for Fourier extension estimate to fractional surface Di, Boning Liu, Ning Yan, Dunyan Classical Analysis and ODEs Analysis of PDEs This article investigates the Fourier extension operator associated with the fractional surface $(ξ,|ξ|^α)$ for $α\geq 2$. We show that the relevant $L^p\to L^q$ Fourier extension inequality possesses extremals for all exponents $p\in[1,2]$. Moreover, for all $p\in(1,2]$, the corresponding $L^p$-extremal sequences are precompact up to symmetries. |
| title | On $L^p$ extremals for Fourier extension estimate to fractional surface |
| topic | Classical Analysis and ODEs Analysis of PDEs |
| url | https://arxiv.org/abs/2406.10693 |