Article ID Journal Published Year Pages File Type
4669249 Bulletin des Sciences Mathématiques 2010 7 Pages PDF
Abstract

In this paper we study the Riesz transform on complete and connected Riemannian manifolds M with a certain spectral gap in the L2 spectrum of the Laplacian. We show that on such manifolds the Riesz transform is Lp bounded for all p∈(1,∞). 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 L2 spectrum of the Laplacian.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)