Restriction of Fractional Derivatives of the Fourier Transform
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914985233350656 |
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| author | Goldberg, Michael Lau, Chun Ho |
| author_facet | Goldberg, Michael Lau, Chun Ho |
| contents | In this paper, we showed that for suitable $(β,p, s,\ell)$ the $β$-order fractional derivative with respect to the last coordinate of the Fourier transform of an $L^p(\mathbb{R}^n)$ function is in $H^{-s}$ after restricting to a graph of a function with non-vanishing Gaussian curvature provided that the restriction of the Fourier transform of such function to the surface is in $H^{\ell}$. This is a generalization of the result in \cite{GoldStol}*{Theorem 1.12}. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_06092 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restriction of Fractional Derivatives of the Fourier Transform Goldberg, Michael Lau, Chun Ho Functional Analysis Classical Analysis and ODEs 42B10, 42B20 In this paper, we showed that for suitable $(β,p, s,\ell)$ the $β$-order fractional derivative with respect to the last coordinate of the Fourier transform of an $L^p(\mathbb{R}^n)$ function is in $H^{-s}$ after restricting to a graph of a function with non-vanishing Gaussian curvature provided that the restriction of the Fourier transform of such function to the surface is in $H^{\ell}$. This is a generalization of the result in \cite{GoldStol}*{Theorem 1.12}. |
| title | Restriction of Fractional Derivatives of the Fourier Transform |
| topic | Functional Analysis Classical Analysis and ODEs 42B10, 42B20 |
| url | https://arxiv.org/abs/2410.06092 |