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