The higher order Riesz transform and BMO type space associated to Schrödinger operators

Let L = −Δ + V be a Schrödinger operator on \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {R}^n$\end{document} ( n ≥ 3), where \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$V \not\equiv 0$\end{document} is a nonnegative potential belonging to certain reverse Hölder class B s for \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$s \ge \frac{n}{2}$\end{document} . In this article, we prove the boundedness of some integral operators related to L , such as L −1 ∇ 2 , L −1 V and L −1 ( − Δ) on the space \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$BMO_L(\mathbb {R}^n)$\end{document} .