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In this paper, we prove the $M^k$-type sharp maximal function estimates for the commutators related to some singular integral operators satisfying a variant of Hörmander's condition.  As an application, we obtain the weighted boundedness of the commutators on Lebesgue and Morrey spaces

boletim da sociedade paranaense de matemática

$M^2$-type sharp estimates and weighted boundedness for commutators related to singular integral operators satisfying a variant of Hörmander's condition