On fractional integrals generated by Radon transforms over paraboloids

Author:

Rubin Boris1

Affiliation:

1. Department of Mathematics , Louisiana State University , Baton Rouge , LA 70803 , USA

Abstract

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^{p}} - L q {L^{q}} estimates for the Radon transform and more general convolution-type fractional integrals with the kernels having singularity on the paraboloids.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Reference35 articles.

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5. M. Christ, Extremizers of a Radon transform inequality, Advances in Analysis: The Legacy of Elias M. Stein, Princeton Math. Ser. 50, Princeton University, Princeton (2014), 84–107.

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