Riesz transform on locally symmetric spaces and Riemannian manifolds with a spectral gap期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Riesz transform on locally symmetric spaces and Riemannian manifolds with a spectral gap

Authors:	Lizhen Ji Peer Kunstmann

Affiliation:	^a Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China ^b Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA ^c Institut für Analysis, Universität Karlsruhe (TH), Kaiserstr. 89-93, 76128 Karlsruhe, Germany ^d Institut für Algebra und Geometrie, Universität Karlsruhe (TH), Kaiserstr. 89-93, 76128 Karlsruhe, Germany

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.

Keywords:	Riesz transform on Riemannian manifolds Spectral gap
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