Journal of Geometric Analysis

, Volume 18, Issue 1, pp 192–248

Hardy Spaces of Differential Forms on Riemannian Manifolds

Article

Abstract

Let M be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces Hp of differential forms on M and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the Hp-boundedness for Riesz transforms on M, generalizing previously known results. Further applications, in particular to H functional calculus and Hodge decomposition, are given.

Keywords

Riemannian manifolds Hardy spaces Differential forms Riesz transforms 

Mathematics Subject Classification (2000)

42B30 58J05 47F05 47A60 

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Copyright information

© Mathematica Josephina, Inc. 2007

Authors and Affiliations

  1. 1.Université de Paris-Sud, Orsay et CNRS UMR 8628Orsay CedexFrance
  2. 2.Centre for Mathematics and its Applications, Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia
  3. 3.LATP, CNRS UMR 6632, Faculté des Sciences et TechniquesUniversité Paul CézanneMarseille Cedex 20France

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