Restriction of Fractional Derivatives of the Fourier Transform
| Autor: | Goldberg, Michael, Lau, Chun Ho |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we showed that for suitable $(\beta,p, s,\ell)$ the $\beta$-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}. Comment: Fixed the description of Figure 3 and 4 |
| Databáze: | arXiv |
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