Hardy spaces associated to nonnegative self-adjoint operators satisfying Davies-Gaffney estimates

Abstract. Let X be a metric space with doubling measure, and L be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on L2(X). In this article we present a theory of Hardy and BMO spaces as-sociated to L, including an atomic (or molecular) decomposition, square function characterization, and duality of Hardy and BMO spaces. Fur-ther specializing to the case that L is a Schrödinger operator on Rn with a non-negative, locally integrable potential, we establish additional characterizations of such Hardy spaces in terms of maximal functions. Finally, we define Hardy spaces HpL(X) for p> 1, which may or may not coincide with the space Lp(X), and show that they interpolate with H1L(X) spaces by the complex method. The authors gratefully acknowledge support from NSF as follows: S. Hofmann (DM