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

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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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Classical Analysis and ODEs, 44A12; 35S30

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http://salesiana.dossiersoluciones.com/handle/123456789/69618

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312307
 http://arxiv.org/abs/math/0312307

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arXiv