Weighted norm inequalities for Schrödinger type operators

Abstract

Let $L=-\hat{I}”+V$ be a Schrödinger operator, where $\hat{I}”$ is the Laplacian operator on $\rz$, while nonnegative potential $V$ belongs to the reverse Hölder class. In this paper, we establish the weighted norm inequalities for some Schrödinger type operators, which include Riesz transforms and fractional integrals and their commutators. These results generalize substantially some well-known results.