Mathematics – Differential Geometry
Scientific paper
2006-11-11
Mathematics
Differential Geometry
Scientific paper
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 $H^{\infty}$ functional calculus and Hodge decomposition, are given.
Auscher Pascal
McIntosh Alan
Russ Emmanuel
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