Riesz Transform on Locally Symmetric Spaces and Riemannian Manifolds with a Spectral Gap

Lizhen Ji; Peer Kunstmann; Andreas Weber

doi:10.1016/j.bulsci.2009.09.003

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arXiv · 1005.2975

Riesz Transform on Locally Symmetric Spaces and Riemannian Manifolds with a Spectral Gap

Lizhen Ji·Peer Kunstmann·Andreas Weber

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Abstract

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.

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BibTeX RIS

Lizhen Ji, Peer Kunstmann, Andreas Weber. 2010-05-17. Riesz Transform on Locally Symmetric Spaces and Riemannian Manifolds with a Spectral Gap. https://doi.org/10.1016/j.bulsci.2009.09.003

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