Riesz transforms associated to Schrödinger operators on weighted Hardy spaces

Let w be some Ap weight and enjoy reverse Hölder inequality, and let L=− + V be a Schrödinger operator on Rn, where V ∈ L1 loc(Rn) is a non-negative function on Rn. In this article we introduce weighted Hardy spaces H1 L,w(Rn) associated to L in terms of the area function characterization, and prove their atomic characters. We show that the Riesz transform ∇L−1/2 associated to L is bounded on L p w(Rn) for 1