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

Shaoming Guo, Alex Iosevich, Ruixiang Zhang +1

We prove that if $f\in L^p({\mathbb{R}}^k)$ with $p<(k^2+k+2)/2$ satisfies that $\hat{f}$ is supported on a small perturbation of the moment curve in ${\mathbb{R}}^k$, then $f$ is…