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

Luca Brandolini·Allan Greenleaf·Giancarlo Travaglini
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Abstract

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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Luca Brandolini, Allan Greenleaf, Giancarlo Travaglini. 2003-12-16. $L^p - L^{p'}$ estimates for overdetermined Radon transforms. https://arxiv.org/abs/math/0312307

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