Calculus of Variations and Geometric Measure Theory

G. Del Nin - A. Merlo

Endpoint Fourier restriction and unrectifiability

created by delnin on 22 Apr 2021
modified on 21 Sep 2021


Accepted Paper

Inserted: 22 apr 2021
Last Updated: 21 sep 2021

Journal: Proc. Amer. Math. Soc.
Year: 2021

ArXiv: 2104.07482 PDF


We show that if a measure of dimension $s$ on $\mathbb{R}^d$ admits $(p,q)$ Fourier restriction for some endpoint exponents allowed by its dimension, namely $q=\tfrac{s}{d}p'$ for some $p>1$, then it is either absolutely continuous or $1$-purely unrectifiable.