Weighted estimates for commutators of some singular integrals related to Schrödinger operators

Let L=−Δ+V$L=-\mathrm{\Delta }+V$ be a Schrödinger operator with a non-negative potential V satisfying some appropriate reverse Hölder inequality. In this paper, we study the boundedness of the commutators of some singular integrals associated to L such as the Riesz transforms and fractional integrals with the new BMO functions introduced in Bongioanni et al. (2011) 1] on the weighted spaces L^p(w)$L^p(w)$ where w belongs to the new classes of weights introduced by Bongioanni et al. (2011) 2].