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

Shaoming Guo; Alex Iosevich; Ruixiang Zhang; Pavel Zorin-Kranich

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

Classical Analysis and ODEs 2023-11-21 v1

Authors: Shaoming Guo , Alex Iosevich , Ruixiang Zhang , Pavel Zorin-Kranich

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.

Keywords

l^p integrability fourier support moment curve smooth space curve unique continuation

Cite

@article{arxiv.2311.11529,
  title  = {$L^p$ integrability of functions with Fourier support on a smooth space curve},
  author = {Shaoming Guo and Alex Iosevich and Ruixiang Zhang and Pavel Zorin-Kranich},
  journal= {arXiv preprint arXiv:2311.11529},
  year   = {2023}
}

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

Abstract

Keywords

Cite

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