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Hardy Spaces of Differential Forms on Riemannian Manifolds

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Abstract

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

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Authors and Affiliations

  1. Université de Paris-Sud, Orsay et CNRS UMR 8628, 91405, Orsay Cedex, France

    Pascal Auscher

  2. Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra, ACT, 0200, Australia

    Alan McIntosh

  3. LATP, CNRS UMR 6632, Faculté des Sciences et Techniques, Université Paul Cézanne, Case cour A, Avenue Escadrille Normandie-Niémen, 13397, Marseille Cedex 20, France

    Emmanuel Russ

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  1. Pascal Auscher
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  2. Alan McIntosh
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  3. Emmanuel Russ
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Correspondence to Pascal Auscher.

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Auscher, P., McIntosh, A. & Russ, E. Hardy Spaces of Differential Forms on Riemannian Manifolds. J Geom Anal 18, 192–248 (2008). https://doi.org/10.1007/s12220-007-9003-x

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