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

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

2003-12-16

arxiv.org/abs/math/0312307v1

Mathematics

Classical Analysis and ODEs

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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