Averaged decay estimates for Fourier transforms of measures over curves with non vanishing torsion

TL;DR

This paper investigates decay rates of Fourier transforms of measures averaged over space curves with non-zero torsion, extending known results to higher dimensions and analyzing the sharpness of these decay estimates.

Contribution

It introduces new decay estimates for Fourier transforms over space curves with torsion in higher dimensions, advancing the understanding of such transforms.

Findings

Extended decay estimates to higher dimensions

Demonstrated the sharpness of the decay bounds

Provided new insights into Fourier analysis over curved measures

Abstract

We study averaged decay estimates for Fourier transforms of measures when the averages are taken over space curves with non-vanishing torsion. We extend the previously known results to higher dimensions and discuss sharpness of the estimates.