%0 Journal Article
%T $L^p$-nondegenerate Radon-like operators with vanishing rotational curvature
%A Philip T. Gressman
%J Mathematics
%D 2013
%I arXiv
%X We consider the $L^p \rightarrow L^q$ mapping properties of a model family of Radon-like operators integrating functions over n-dimensional submanifolds of ${\mathbb R}^{2n}$. It is shown that nonvanishing rotational curvature is never generic when $n \geq 2$ and is, in fact, impossible for all but finitely many values of $n$. Nevertheless, operators satisfying the same $L^p \rightarrow L^q$ estimates as the "nondegenerate" case (modulo the endpoint) are dense in the model family for all $n$.
%U http://arxiv.org/abs/1308.1387v1