Restriction estimates for one class of hypersurfaces with vanishing curvature in ${\mathbb{R}}^n$

Abstract

In this paper, we study the restriction problem for one class of hypersurfaces with vanishing curvature in ${\mathbb{R}}^n$ with $n$ being odd. We obtain an $L^2-L^p$ restriction estimate, which is optimal except at the endpoint. Furthermore, we establish an $L^s-L^p$ restriction estimate for these hypersurfaces, which is achieved by improving the known $L^{\infty }$ restriction estimate for hypersurfaces with $\frac{n-1}{2}$ positive principal curvatures and $\frac{n-1}{2}$ negative principal curvatures.

18 pages, 3 figures

References in corpus (1)

• A note on Fourier restriction and nested Polynomial Wolff axioms