Title

Riesz potentials and orthogonal radon transforms on affine grassmannians

Document Type

Article

Publication Date

4-1-2021

Abstract

We establish intertwining relations between Riesz potentials associated with fractional powers of minus-Laplacian and orthogonal Radon transforms Rj,k of the Gonzalez-Strichartz type. The latter take functions on the Grassmannian of j-dimensional affine planes in Rn to functions on a similar manifold of k-dimensional planes by integration over the set of all j-planes that meet a given k-plane at a right angle. The main results include sharp existence conditions of Rj,kf on Lp-functions, Fuglede type formulas connecting Rj,k with Radon-John k-plane transforms and Riesz potentials, and explicit inversion formulas for Rj,kf under the assumption that f belongs to the range of the j-plane transform. The method extends to another class of Radon transforms defined on affine Grassmannians by inclusion.

Publication Source (Journal or Book title)

Fractional Calculus and Applied Analysis

First Page

376

Last Page

392

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