On the Fourier transform of measures in Besov spaces

Abstract We prove quantitative estimates for the decay of the Fourier transform of the Riesz potential of measures that are in homogeneous Besov spaces of the negative exponent: where with and is the Riesz potential of of order . Our results are naturally applicable to the Morrey space , including for example the Frostman measure of any compact set with for some . When for , , and , our results extend the work of Herz and Ko–Lee. We provide examples which show the sharpness of our results.