Fractional integrals associated with Radon transforms

We obtain sharp Lp-Lq estimates for fractional integrals generated by Radon transforms of the following three types: The classical Radon transform over the set of all hyperplanes in ℝn, the Strichartz transversal transform over only those hyperplanes which meet the last coordinate axis, and the Radon transform associated with paraboloids. The method relies on a version of Stein's interpolation theorem for analytic families of operators communicated by L. Grafakos.