Weighted norm estimates for the Semyanistyi fractional integrals and Radon transforms

2012/10/19 by Boris Rubin, Rubin, Boris
Mathematics · #44A12 #47G10 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:44A12 #msc:47G10

paper · pdf · doi:10.48550/arxiv.1210.5414

13 pages

arxiv created 2012/10/19 · arxiv updated 2012/10/22

Abstract

Semyanistyi's fractional integrals have come to analysis from integral geometry. They take functions on Rⁿ to functions on hyperplanes, commute with rotations, and have a nice behavior with respect to dilations. We obtain sharp inequalities for these integrals and the corresponding Radon transforms acting on L^p spaces with a radial power weight. The operator norms are explicitly evaluated. Similar results are obtained for fractional integrals associated to k-plane transforms for any 1≤ k<n.

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