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We establish pointwise sparse dominations for the iterated commutators of multi(sub)linear operators satisfying the W q $W_{q}$ 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.

Some remarks on the sparse dominations for commutators of multi(sub)linear operator