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

Abstract

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) 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.