Orlicz–Hardy spaces associated to operators satisfying bounded 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 H L , ω ( X ) . Finally, we show that L has a bounded holomorphic functional calculus in H L , ω ( X ) and the Riesz transform is bounded from H L , ω ( X ) to L ( ω ) .