$L^p - L^{p'}$ estimates for overdetermined Radon transforms

Mathematics – Classical Analysis and ODEs

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Scientific paper

We prove several variations on the results of Ricci and Travaglini concerning
bounds for convolution with all rotations of a measure supported by a fixed
convex curve in the plane. Estimates are obtained for averages over
higher-dimensional convex hypersurfaces, smooth k-dimensional surfaces and
non-translation invariant families of surfaces.

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