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.
Basak et al. (Tue,) studied this question.