Existence of extremizers for Fourier restriction to the moment curve

TL;DR

This paper proves that Fourier restriction and extension operators related to the moment curve have extremizers, and extremizing sequences are precompact up to symmetries, advancing understanding of Fourier analysis on curves.

Contribution

It establishes the existence of extremizers for Fourier restriction to the moment curve and shows precompactness of extremizing sequences, a novel result in harmonic analysis.

Findings

Existence of extremizers for the restriction and extension operators.

Precompactness of extremizing sequences modulo symmetries.

Advancement in understanding Fourier analysis on the moment curve.

Abstract

We show that the restriction and extension operators associated to the moment curve possess extremizers and that $L^p$-normalized extremizing sequences of these operators are precompact modulo symmetries.