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