%0 Journal Article
%T Riesz Transform on Locally Symmetric Spaces and Riemannian Manifolds with a Spectral Gap
%A Lizhen Ji
%A Peer Kunstmann
%A Andreas Weber
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.bulsci.2009.09.003
%X In this paper we study the Riesz transform on complete and connected Riemannian manifolds $M$ with a certain spectral gap in the $L^2$ spectrum of the Laplacian. We show that on such manifolds the Riesz transform is $L^p$ bounded for all $p \in (1,\infty)$. This generalizes a result by Mandouvalos and Marias and extends a result by Auscher, Coulhon, Duong, and Hofmann to the case where zero is an isolated point of the $L^2$ spectrum of the Laplacian.
%U http://arxiv.org/abs/1005.2975v1