Weighted norm inequalities for commutators of Littlewood-Paley functions related to Schrödinger operators

Abstract

Let $L=-\hat{I}”+V$ be a Schrödinger operator, where $\hat{I}”$ is the Laplacian operator on $\rz$, while the nonnegative potential $V$ belongs to certain reverse Hölder class. In this paper, we establish some weighted norm inequalities for commutators of Littlewood-Paley functions related to Schrödinger operators.