English

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)