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arXiv · 1901.06835

Some notes on commutators of the fractional maximal function on variable Lebesgue spaces

Pu Zhang·Zengyan Si·Jianglong Wu
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Abstract

Let $0<α<n$ and $M_α$ be the fractional maximal function. The nonlinear commutator of $M_α$ and a locally integrable function $b$ is given by $[b,M_α](f)=bM_α(f)-M_α(bf)$. In this paper, we mainly give some necessary and sufficient conditions for the boundedness of $[b,M_α]$ on variable Lebesgue spaces when $b$ belongs to Lipschitz or $BMO(\rn)$ spaces, by which some new characterizations for certain subclasses of Lipschitz and $BMO(\rn)$ spaces are obtained.

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Pu Zhang, Zengyan Si, Jianglong Wu. 2019-01-21. Some notes on commutators of the fractional maximal function on variable Lebesgue spaces. https://doi.org/10.1186/s13660-019-1960-7

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