SHARP RATE OF AVERAGE DECAY OF THE FOURIER TRANSFORM OF A BOUNDED SET

Abstract. Estimates for the decay of Fourier transforms of measures have extensive applica-tions in numerous problems in harmonic analysis and convexity including the distribution of lattice points in convex domains, irregularities of distribution, generalized Radon transforms and others. Here we prove that the spherical L2-average decay rate of the Fourier transform of the Lebesgue measure on an arbitrary bounded convex set in Rd i