A Fourier Restriction Theorem For A Twodimensional Surface Of Finite Type

Abstract

The problem of $L^p(R^3)\to L^2(S)$ Fourier restriction estimates for smooth hypersurfaces S of finite type in R^3 is by now very well understood for a large class of hypersurfaces, including all analytic ones. In this article, we take up the study of more general $L^p(R^3)\to L^q(S)$ Fourier restriction estimates, by studying a prototypical class of two-dimensional surfaces with strongly varying curvature conditions. Our approach is based on an adaptation of the so-called bilinear method. We discuss several new features arising in the study of this problem.

Cited by in corpus (4)

• Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System
• Restriction estimates for certain surfaces of finite type in ${\mathbb{R}}^3$
• A sharp Lp Lq Fourier restriction theorem for a conical surface of finite type
• Restriction estimates for one class of hypersurfaces with vanishing curvature in ${\mathbb{R}}^n$