Orlicz–Hardy spaces associated to operators satisfying bounded H∞ functional calculus and Davies–Gaffney estimates

Let X be a metric space with doubling measure, and L be an operator which has a bounded H∞ functional calculus and satisfies Davies–Gaffney estimates. In this paper, we develop a theory of Orlicz–Hardy spaces associated to L, including a molecule decomposition, square function characterization and duality of Orlicz–Hardy spaces HL,ω(X). Finally, we show that L has a bounded holomorphic functional calculus in HL,ω(X) and the Riesz transform is bounded from HL,ω(X) to L(ω).