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arXiv · 2102.01277

On weighted compactness of commutators of Schr\"{o}dinger operators

Qianjun He·Pengtao Li
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Abstract

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

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Qianjun He, Pengtao Li. 2021-02-02. On weighted compactness of commutators of Schr\"{o}dinger operators. https://arxiv.org/abs/2102.01277

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