Multilinear Commutators of Multilinear Square Operators Associated with New $BMO$ Functions and New Weight Functions

Via the new weight $A_{\vec{p}}^{\mathrm{\infty }}(\phi )$ 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.