Hardy spaces associated to operators satisfying Davies–Gaffney estimates and bounded holomorphic functional calculus

Let X be a space of homogeneous type. Assume that an operator L has a bounded holomorphic functional calculus on L2(X) and the kernel of the heat semigroup {e−tL}t>0 satisfies the Davies–Gaffney estimates. Without the assumption that L is self-adjoint, we develop a theory of Hardy spaces , 00 and certain Riesz transforms associated to L are bounded from to Lp(X) for all 0