RIESZ POTENTIALS AND ORTHOGONAL RADON TRANSFORMS ON AFFINE GRASSMANNIANS

被引:1
|
作者
Rubin, Boris [1 ]
Wang, Yingzhan [2 ]
机构
[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA
[2] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Peoples R China
基金
中国国家自然科学基金;
关键词
Riesz potentials; Erdelyi-Kober fractional integrals; Radon transforms; Grassmann manifolds; INTEGRALS;
D O I
10.1515/fca-2021-0017
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We establish intertwining relations between Riesz potentials associated with fractional powers of minus-Laplacian and orthogonal Radon transforms R-j,R-k of the Gonzalez-Strichartz type. The latter take functions on the Grassmannian of j-dimensional affine planes in R-n 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 R(j,k)f on L-p-functions, Fuglede type formulas connecting R-j,R-k with Radon-John k-plane transforms and Riesz potentials, and explicit inversion formulas for R(j,k)f 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.
引用
收藏
页码:376 / 392
页数:17
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