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arXiv · 1708.09549

Necessary and sufficient conditions for boundedness of commutators of bilinear Hardy-Littlewood maximal function

Dinghuai Wang·Jiang Zhou
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Abstract

Let $\mathcal{M}$ be the bilinear Hardy-Littlewood maximal function and $\vec{b}=(b,b)$ be a collection of locally integrable functions. In this paper, the authors establish characterizations of the weighted {\rm BMO} space in terms of several different commutators of bilinear Hardy-Littlewood maximal function, respectively; these commutators include the maximal iterated commutator $\mathcal{M}_{Π\vec{b}}$, the maximal linear commutator $\mathcal{M}_{Σ\vec{b}}$, the iterated commutator $[Π\vec{b},\mathcal{M}]$ and the linear commutator $[Σ\vec{b},\mathcal{M}]$.

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Dinghuai Wang, Jiang Zhou. 2017-08-31. Necessary and sufficient conditions for boundedness of commutators of bilinear Hardy-Littlewood maximal function. https://arxiv.org/abs/1708.09549

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