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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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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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