Hardy spaces of differential forms on Riemannian manifolds

Auscher, Pascal; Mcintosh, Alan; Russ, Emmanuel

Hardy spaces of differential forms on Riemannian manifolds

Authors

Auscher, Pascal

Mcintosh, Alan

Russ, Emmanuel

Description

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.