Journal of Geometric Analysis

, Volume 18, Issue 1, pp 192–248

Hardy Spaces of Differential Forms on Riemannian Manifolds

Article

DOI: 10.1007/s12220-007-9003-x

Cite this article as:
Auscher, P., McIntosh, A. & Russ, E. J Geom Anal (2008) 18: 192. doi:10.1007/s12220-007-9003-x

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 manifoldsHardy spacesDifferential formsRiesz transforms

Mathematics Subject Classification (2000)

42B3058J0547F0547A60

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