On Fractional Integrals Generated by Radon Transforms over Paraboloids

Abstract

We apply the Fourier transform technique and a modified version of E. Stein's interpolation theorem communicated by L. Grafakos, to obtain sharp $L^p$-$L^q$ estimates for the Radon transform and more general convolution-type fractional integrals with the kernels having singularity on the paraboloids.

27 pages. arXiv admin note: text overlap with arXiv:2208.09080