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On Weighted Compactness of Commutators Related with Schrödinger Operators

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Abstract

Let \({\cal L} = - \Delta + V\) be a Schrödinger operator, where Δ is the Laplacian operator on ℝd (d ≥ 3), while the nonnegative potential V belongs to the reverse Hölder class Bq, q > d/2. In this paper, we study weighted compactness of commutators of some Schrödinger operators, which include Riesz transforms, standard Calderón—Zygmund operators and Littlewood—Paley functions. These results substantially generalize some well-known results.

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Acknowledgements

The authors cordially thank the referees and the editors for their careful reading of the paper and valuable comments which led to the great improvement of the paper.

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Authors and Affiliations

  1. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, P. R. China

    Qian Jun He

  2. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, P. R. China

    Peng Tao Li

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  1. Qian Jun He
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  2. Peng Tao Li
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Correspondence to Peng Tao Li.

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This work was in part supported by National Natural Science Foundation of China (Grant Nos. 11871293, 11871452, 12071473, 12071272) and Shandong Natural Science Foundation of China (Grant No. ZR2017JL008)

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He, Q.J., Li, P.T. On Weighted Compactness of Commutators Related with Schrödinger Operators. Acta. Math. Sin.-English Ser. 38, 1015–1040 (2022). https://doi.org/10.1007/s10114-022-1081-y

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  • DOI: https://doi.org/10.1007/s10114-022-1081-y

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