Commutators of multilinear Calderón–Zygmund operators with kernels of Dini’s type on generalized weighted Morrey spaces and applications

Let T be a multilinear Calderón–Zygmund operator of type $$\omega $$ with $$\omega $$ being nondecreasing and satisfying a kind of Dini’s type condition and $$T_{\Pi \vec {b}}$$ be the iterated commutators of the operator T with $$BMO^m$$ functions. The generalized weighted Morrey strong and weak $$L(\log L)$$ -type endpoint estimates for T and $$T_{\Pi \vec {b}}$$ with multiple weights are established. As applications multiple weighted Morrey estimates for iterated commutators of bilinear pseudo-differential operators and paraproducts with mild regularity are given.