Carleson measures for the generalized Schrödinger operator

Abstract

Let $\mathcal{L}=-\Delta +\mu$ be the generalized Schrödinger operator on ${\mathbb{R}}^n$, $n\ge 3$, where $\Delta$ is the Laplacian and $\mu \not\equiv 0$ is a nonnegative Radon measure on ${\mathbb{R}}^n$. In this article, we give a characterization of ${\mathrm{BMO}}_{\mathcal{L}}$ in terms of Carleson measures, where ${\mathrm{BMO}}_{\mathcal{L}}$ is the $\mathrm{BMO}$-type space associated with the generalized Schrödinger operator.