A perturbation result for the Riesz transform

Baptiste Devyver

paper

A perturbation result for the Riesz transform

arXiv:1105.5999

Abstract

We show a perturbation result for the boundedness of the Riesz transform : if $M$ and $M_{0}$ are complete Riemannian manifolds satisfying a Sobolev inequality of dimension $n$ , which are isometric outside a compact set, and if the Riesz transform on $M_{0}$ is bounded on $L^{q}$ , then for all $\frac{n}{n - 2}, t h e R i esz t r an s f or m o n$ M $i s b o u n d e d o n$ L^p $p r o v i d e d t ha t$ M $i s p - h y p er b o l i c O R$ M$ has only one end.