Weighted norm inequalities for Riesz transforms of magnetic Schrödinger operators

Abstract

Let $A=-(\nabla-i\vec{a})^2+V$ be a magnetic Schrödinger operator acting on $L^2(\mathbb{R}^n), n\geq 1$, where $\vec{a}=(a_1,\ldots, a_n)\in L^2_{loc}$ and $0\leq V \in L^1_{ loc}$. In this paper we will give weighted $L^p$ estimates for Riesz transforms $(\partial/\partial x_k -ia_k )A^{-1/2}$ associated with $A, k=1, \ldots, n,$ and their commutators with an appropriate range of $p$. Note that our obtained results extend those in [11, 12].