Riesz potentials and orthogonal radon transforms on affine grassmannians
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
Rubin, B., & Wang, Y. (2021). Riesz potentials and orthogonal radon transforms on affine grassmannians. Fractional Calculus and Applied Analysis, 24 (2), 376-392. https://doi.org/10.1515/fca-2021-0017