Weighted inequalities for commutators of Schrödinger-Riesz transforms

Abstract: In this work we obtain weighted $L^p$, $1<p<\infty$, and weak $L\log L$ estimates for the commutator of the Riesz transforms associated to a Schr\"odinger operator $-\lap+V$, where $V$ satisfies some reverse H\"older inequality. The classes of weights as well as the classes of symbols are larger than $A_p$ and $BMO$ corresponding to the classical Riesz transforms.