Riesz transforms associated to Schrödinger operators on weighted Hardy spaces

Let w be some Ap weight and enjoy reverse Hölder inequality, and let L=-Δ+V be a Schrödinger operator on Rn, where V?Lloc1(Rn) is a non-negative function on Rn. In this article we introduce weighted Hardy spaces HL,w1(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 Lwp(Rn) for 1<p<2, and bounded from HL,w1(Rn) to the classical weighted Hardy space Hw1(Rn).