2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66797We 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)Classical Analysis and ODEs42Btext