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On the compactness of oscillation and variation of commutators

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Abstract

In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, we establish a new \({{\mathrm{CMO}}({\mathbb {R}}^{n})}\) characterization via the compactness of oscillation and variation of commutators on weighted Lebesgue spaces.

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Acknowledgements

The authors want to express their sincerely thanks to the referees for their valuable remarks and suggestions, which made this paper more readable.

Funding

This work is supported by the NSF of China (Nos. 11771358, 11701112, 11971402, 11871254), the NSF of Fujian Province of China (No. 2020J01708), the scientific research project of The Education Department of Fujian Province (No. JAT200331), and President’s fund of Minnan Normal University (No. KJ2020020).

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Authors and Affiliations

  1. School of Science, Jimei University, Xiamen, 361021, People’s Republic of China

    Weichao Guo

  2. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, 363000, People’s Republic of China

    Yongming Wen

  3. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China

    Huoxiong Wu & Dongyong Yang

Authors
  1. Weichao Guo
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  2. Yongming Wen
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  3. Huoxiong Wu
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  4. Dongyong Yang
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Corresponding author

Correspondence to Yongming Wen.

Additional information

Communicated by Maria Alessandra Ragusa.

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Guo, W., Wen, Y., Wu, H. et al. On the compactness of oscillation and variation of commutators. Banach J. Math. Anal. 15, 37 (2021). https://doi.org/10.1007/s43037-021-00123-z

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  • DOI: https://doi.org/10.1007/s43037-021-00123-z

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