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.
机构:
Shanxi Normal Univ, Sch Math & Comp Sci, Gongyuanjie Rd, Linfen 041000, Shanxi, Peoples R ChinaShanxi Normal Univ, Sch Math & Comp Sci, Gongyuanjie Rd, Linfen 041000, Shanxi, Peoples R China
机构:
Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
Mem Univ, Dept Math & Stat, St John, NF A1C 5S7, CanadaHunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China
机构:
Seconda Univ Napoli SUN, Dipartimento Matemat, I-81100 Caserta, ItalySeconda Univ Napoli SUN, Dipartimento Matemat, I-81100 Caserta, Italy
Dentice, Eva Ferrara
Lo Re, Pia Maria
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机构:
Univ Naples Federico 2, Dipartimento Matemat R Caccioppoli, I-80126 Naples, ItalySeconda Univ Napoli SUN, Dipartimento Matemat, I-81100 Caserta, Italy