Weighted norm inequalities for Schrödinger type operators

Abstract: Let $L=-\Delta+V$ be a Schr\"{o}dinger operator, where $\Delta $ is the Laplacian operator on $\rz$, while nonnegative potential $V$ belongs to the reverse H\"{o}lder class. In this paper, we establish the weighted norm inequalities for some Schr\"odinger type operators, which include Riesz transforms and fractional integrals and their commutators. These results generalize substantially some well-known results.