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Multilinear commutators of multilinear square operators associated with new $BMO$ functions and new weight functions

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Via the new weight $ A_{\vec p}^{\infty } (\varphi ) $ and the new $ BMO $ function, the authors introduce a new class of multilinear square operators $ T $ with generalized kernels. The boundedness of multilinear commutators and multilinear iterative commutators generated by $ T $ and the new $ BMO $ function on weighted Lebesgue spaces and weighted Morrey spaces is obtained, respectively. The results of this article contain some known conclusions.

Abstract

Via the new weight $ A_{\vec p}^{\infty } (\varphi ) $ and the new $ BMO $ function, the authors introduce a new class of multilinear square operators $ T $ with generalized kernels. The boundedness of multilinear commutators and multilinear iterative commutators generated by $ T $ and the new $ BMO $ function on weighted Lebesgue spaces and weighted Morrey spaces is obtained, respectively. The results of this article contain some known conclusions.

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