Abstract
Let \(b\) be a locally integrable function and \(\mathfrak{M}\) be the bilinear maximal function
In this paper, characterization of the BMO function in terms of commutator \(\mathfrak{M}^{(1)}_{b}\) is established. Also, we obtain the necessary and sufficient conditions for the boundedness of the commutator \([b, \mathfrak{M}]_{1}\). Moreover, some new characterizations of Lipschitz and non-negative Lipschitz functions are obtained.
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I would like to thank the referee for the helpful comment which improved the presentation of this paper.
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This work was supported by National Natural Science Foundation of China (No. 12101010) and Natural Science Foundation of China of Anhui Province (No. 2108085QA19).
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Zhao, H., Wang, D. On functions of bounded mean oscillation with bounded negative part. Anal Math 50, 717–730 (2024). https://doi.org/10.1007/s10476-024-00018-9
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DOI: https://doi.org/10.1007/s10476-024-00018-9