English

$L^p - L^{p'}$ 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.

Keywords

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}
}