On weighted compactness of commutators of Schrödinger operators

Let $\mathcal{L}=-Δ+\mathit{V}(x)$ be a Schrödinger operator, where $Δ$ is the Laplacian operator on $\mathbb{R}^{d}$ $(d\geq 3)$, while the nonnegative potential $\mathit{V}(x)$ 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.

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