Weighted norm inequalities for commutators of Littlewood-Paley functions related to Schr\"odinger operators

Let $L=-\mathrm{\Delta }+V$ be a Schr"{o}dinger operator, where $\mathrm{\Delta }$ is the Laplacian operator on $\text{rz}$, while the nonnegative potential $V$ belongs to certain reverse H"{o}lder class. In this paper, we establish some weighted norm inequalities for commutators of Littlewood-Paley functions related to Schr"odinger operators.