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arXiv · 2408.10245

Characterization of BMO spaces via commutators of fractional maximal function on Lorentz spaces

Heng Yang·Jiang Zhou
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Abstract

Let $0 \leq \alpha<n$ and $b$ be the locally integrable function. In this paper, we consider the maximal commutator of fractional maximal function $M_{b,\alpha}$ and the nonlinear commutator of fractional maximal function $[b, M_{\alpha}]$ on Lorentz spaces. We give some necessary and sufficient conditions for the boundedness of the commutators $M_{b,\alpha}$ and $[b, M_{\alpha}]$ on Lorentz spaces when the function $b$ belongs to BMO spaces, by which some new characterizations of certain subclasses of BMO spaces are obtained.

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Heng Yang, Jiang Zhou. 2024-08-05. Characterization of BMO spaces via commutators of fractional maximal function on Lorentz spaces. https://arxiv.org/abs/2408.10245

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