A Fourier restriction theorem based on convolution powers

TL;DR

This paper establishes a Fourier restriction theorem leveraging convolution powers of measures with integrable densities, advancing understanding of Fourier analysis under specific convolution conditions.

Contribution

It introduces a new Fourier restriction estimate based on the integrability of convolution powers of measures, providing a novel approach in harmonic analysis.

Findings

Proves a Fourier restriction estimate under convolution power assumptions

Demonstrates the role of $r$-integrable densities in restriction theorems

Extends classical Fourier analysis results with convolution-based conditions

Abstract

We prove a Fourier restriction estimate under the assumption that certain convolution power of the measure admits an $r$-integrable density.