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arXiv · 2311.11529

$L^p$ integrability of functions with Fourier support on a smooth space curve

Shaoming Guo·Alex Iosevich·Ruixiang Zhang·Pavel Zorin-Kranich
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Abstract

We prove that if $f\in L^p(\mathbb{R}^k)$ with $p<(k^2+k+2)/2$ satisfies that $\widehat{f}$ is supported on a small perturbation of the moment curve in $\mathbb{R}^k$, then $f$ is identically zero. This improves the more general result of Agranovsky and Narayanan, and the exponents are sharp in all dimensions. In the process, we develop a mechanism that should lead to further progress on related problems.

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Shaoming Guo, Alex Iosevich, Ruixiang Zhang, Pavel Zorin-Kranich. 2023-11-20. $L^p$ integrability of functions with Fourier support on a smooth space curve. https://arxiv.org/abs/2311.11529

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