$L^2$ affine Fourier restriction theorems for smooth surfaces in $\mathbb{R}^3$
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929581034831872 |
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| author | Li, Jianhui |
| author_facet | Li, Jianhui |
| contents | We prove sharp $L^2$ Fourier restriction inequalities for compact, smooth surfaces in $\mathbb{R}^3$ equipped with the affine surface measure or a power thereof. The results are valid for all smooth surfaces and the bounds are uniform for all surfaces defined by the graph of polynomials of degrees up to $d$ with bounded coefficients. The primary tool is a decoupling theorem for these surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_15015 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | $L^2$ affine Fourier restriction theorems for smooth surfaces in $\mathbb{R}^3$ Li, Jianhui Classical Analysis and ODEs 42B99 (Primary), 53A05 (Secondary) We prove sharp $L^2$ Fourier restriction inequalities for compact, smooth surfaces in $\mathbb{R}^3$ equipped with the affine surface measure or a power thereof. The results are valid for all smooth surfaces and the bounds are uniform for all surfaces defined by the graph of polynomials of degrees up to $d$ with bounded coefficients. The primary tool is a decoupling theorem for these surfaces. |
| title | $L^2$ affine Fourier restriction theorems for smooth surfaces in $\mathbb{R}^3$ |
| topic | Classical Analysis and ODEs 42B99 (Primary), 53A05 (Secondary) |
| url | https://arxiv.org/abs/2210.15015 |