Alan McIntosh

Hardy spaces of differential forms on Riemannian manifolds

Let M be a complete Riemannian manifold. Assuming the doubling condition on the volume of balls, we define Hardy spaces H^p of differential forms on M and give various characterisations of them, including a molecular decomposition. As a consequence, we derive the H^p-boundedness for Riesz transforms on M, generalising previously known results. Further applications, in particular to functional calculus and Hodge decomposition, are given. This is joint work with Pascal Auscher and Emmanuel Russ.