Uniform estimates for Fourier restriction to polynomial curves in $\mathbb R^d$

TL;DR

This paper establishes uniform bounds for Fourier restriction operators associated with polynomial curves in Euclidean space, confirming conjectured estimates within a specific range of Lebesgue exponents.

Contribution

It provides the first proof of uniform $L^p o L^q$ bounds for Fourier restriction to polynomial curves in $\

Findings

Proved uniform $L^p o L^q$ bounds for polynomial curves

Confirmed conjectured restriction estimates in the specified range

Extended Fourier restriction theory to polynomial curves in higher dimensions

Abstract

We prove uniform $L^p \to L^q$ bounds for Fourier restriction to polynomial curves in $\mathbb R^d$ with affine arclength measure, in the conjectured range.