Sharp rate of average decay of the Fourier transform of a bounded set
arXiv:math/0303188
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.
10 pages. GAFA (to appear)