Hardy Spaces of Differential Forms on Riemannian Manifolds |
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| Authors: | Pascal Auscher Alan McIntosh Emmanuel Russ |
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| Affiliation: | (1) Université de Paris-Sud, Orsay et CNRS UMR 8628, 91405 Orsay Cedex, France;(2) Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra, ACT, 0200, Australia;(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 |
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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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| Keywords: | Riemannian manifolds Hardy spaces Differential forms Riesz transforms |
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