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

Let X X be a metric space with doubling measure, and L L be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on L 2 ( X ) L^2(X) . In this article we present a theory of Hardy and BMO spaces associated to L L , including an atomic (or molecular) decomposition, square function characterization, and duality of Hardy and BMO spaces. Further specializing to the case that L L is a Schrödinger operator on R n R^n 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 H L p ( X ) H^p_L(X) for p > 1 p>1 , which may or may not coincide with the space L p ( X ) L^p(X) , and show that they interpolate with H L 1 ( X ) H^1_L(X) spaces by the complex method.