Existence of extremizers for Fourier restriction to 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.

arXiv commentIntroduction updated, in particular a section titled "Outline of proof" has been added to improve accessibility, To appear in Trans. Amer. Math. Soc