Sharp rate of average decay of the Fourier transform of a bounded set
Classical Analysis and ODEs
2007-05-23 v1
Abstract
We prove that the spherical mean of the Fourier transform of the characteristic function of a bounded convex set (without any additional assumptions) or a bounded set with a C^{3/2} boundary decays at infinity at the same rate as the Fourier transform of the characteristic function of the ball.
Keywords
Cite
@article{arxiv.math/0303188,
title = {Sharp rate of average decay of the Fourier transform of a bounded set},
author = {L. Brandolini and S. Hofmann and A. Iosevich},
journal= {arXiv preprint arXiv:math/0303188},
year = {2007}
}
Comments
10 pages. GAFA (to appear)