On weighted compactness of commutators of Schrödinger operators

Abstract

Let $\mathcal{L}=-\Delta +V(x)$ be a Schrödinger operator, where $\Delta$ is the Laplacian operator on ${\mathbb{R}}^d$ $(d\ge 3)$, while the nonnegative potential $V(x)$ belongs to the reverse Hölder class $B_q,q>d/2$. In this paper, we study weighted compactness of commutators of some Schrödinger operators, which include Riesz transforms, standard Calderón-Zygmund operatos and Littlewood-Paley functions. These results generalize substantially some well-know results.

25pages