Hardy Spaces of Differential Forms on Riemannian Manifolds

Abstract 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.