We establish pointwise sparse dominations for the iterated commutators of multi(sub)linear operators satisfying the $W_{q}$ condition. As consequences, we present some quantitative weighted estimates for the commutators. In addition, we also obtain the Fefferman–Stein inequality, the Coifman–Fefferman inequality, and the local decay estimates regarding the iterated commutators.

中文翻译：

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关于多（次）线性算子的交换子的稀疏控制的一些评论

我们为满足$ W_ {q} $条件的多（子）线性算子的迭代交换子建立了逐点稀疏控制。结果，我们提出了一些换向器的定量加权估计。此外，我们还获得了Fefferman-Stein不等式，Coifman-Fefferman不等式以及关于迭代换向器的局部衰减估计。