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arXiv · 2410.06092

Restriction of Fractional Derivatives of the Fourier Transform

Michael Goldberg·Chun Ho Lau
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Abstract

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}.

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Michael Goldberg, Chun Ho Lau. 2024-10-08. Restriction of Fractional Derivatives of the Fourier Transform. https://arxiv.org/abs/2410.06092

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