$L^p - L^{p'}$ estimates for overdetermined Radon transforms
Classical Analysis and ODEs
2007-05-23 v1
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.
Cite
@article{arxiv.math/0312307,
title = {$L^p - L^{p'}$ estimates for overdetermined Radon transforms},
author = {Luca Brandolini and Allan Greenleaf and Giancarlo Travaglini},
journal= {arXiv preprint arXiv:math/0312307},
year = {2007}
}