Discrete Fourier restriction associated with KdV equations

In this paper, we consider a discrete restriction associated with KdV equations. Some new Strichartz estimates are obtained. We also establish the local well-posedness for the periodic generalized Korteweg-de Vries equation with nonlinear term $F(u){\text{p}}_{x}u$ provided $F\in C^5$ and the initial data $\varphi \in H^s$ with $s>1\mathrm{/}2$.