Hardy Spaces and bmo on Manifolds with Bounded Geometry

We develop the theory of the “local” Hardy space and John-Nirenberg space when M is a Riemannian manifold with bounded geometry, building on the classic work of Fefferman-Stein and subsequent material, particularly of Goldberg and Ionescu. Results include – duality, L ^p estimates on an appropriate variant of the sharp maximal function, and bmo-Sobolev spaces, and action of a natural class of pseudodifferential operators, including a natural class of functions of the Laplace operator, in a setting that unifies these results with results on L ^p -Sobolev spaces. We apply results on these topics to some interpolation theorems, motivated in part by the search for dispersive estimates for wave equations.