A sharp Lp Lq Fourier restriction theorem for a conical surface of finite type

TL;DR

This paper establishes a precise Fourier restriction theorem for a finite type conical surface, advancing the understanding of Fourier analysis on such geometric structures.

Contribution

It provides a sharp restriction theorem for a conical surface of finite type, improving upon previous results by Barcelo.

Findings

Derived a sharp restriction estimate for the conical surface

Enhanced understanding of Fourier transform behavior on finite type cones

Improved bounds over previous theorems

Abstract

We present a restriction theorem for the Fourier transform to a 2-dimensional conical surface of finite type, obtaining a sharp result, which improves previous work by Barcelo.