We establish intertwining relations between Riesz potentials associated with fractional powers of minus-Laplacian and orthogonal Radon transforms 𝓡 j , 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 , 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.

中文翻译：

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仿射Grassmannian上的Riesz势和正交ra变换

我们在与负拉普拉斯分数功率和冈萨雷斯-斯特拉查兹类型的正交Radon变换𝓡j，k有关的里斯势之间建立了相互联系的关系。后者在over n中的j维仿射平面的Grassmannian上起作用，通过对所有以直角满足给定k平面的j平面的集合进行积分，在k维平面的类似流形上起作用。主要结果包括L p函数上的𝓡j，kf的尖锐存在条件，在假定条件下将Rad-k平面变换和Riesz势与𝓡j，k连接的Fuglede型公式以及𝓡j，kf的显式反演公式f属于j平面变换的范围。该方法扩展到通过仿射在仿射Grassmannian上定义的另一类Radon变换。