Hardy spaces of differential forms and Riesz transforms on Riemannian manifolds

Abstract

Let M be a complete Riemannian manifold. Assuming that the Riemannian measure is doubling, we define, for all 1⩽p⩽+∞, a Hardy space Hp(ΛT*M) of differential forms on M , and give two alternative characterizations of H1(ΛT*M). We also prove, for all 1⩽p⩽+∞, the Hp(ΛT*M) boundedness of Riesz transforms on M , and show that Hp(ΛT*M) has a bounded holomorphic functional calculus.