Boundedness of Singular Integrals on Hardy Type Spaces Associated with Schrödinger Operators

Let L=-Δ+V be a Schrödinger operator on Rn,n≥3 , where V≢0 is a nonnegative potential belonging to the reverse Hölder class Bn/2 . The Hardy type spaces HLp, n/(n+δ) <p≤1, for some δ>0 , are defined in terms of the maximal function with respect to the semigroup {e-tL}t>0 . In this paper, we investigate the bounded properties of some singular integral operators related to L , such as Liγ and ∇L-1/2 , on spaces HLp . We give the molecular characterization of HLp , which is used to establish the HLp -boundedness of singular integrals.