, Volume 18, Issue 1, pp 192-248

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.