Endpoint Fourier restriction and unrectifiability

2021/04/15 by Del Nin, Giacomo, Merlo, Andrea
#28A75 (Secondary) #42B10 (Primary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.07482

Abstract

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

Related

• Large sets without Fourier restriction theorems
• A uniform Fourier restriction theorem for surfaces in R^d
• Sets of Salem type and sharpness of the L²-Fourier restriction theorem
• L² restriction estimates from the Fourier spectrum
• Dimension-free Fourier restriction inequalities