Commutators of multilinear Calderón-Zygmund operators with kernels of Dini's type and applications

Abstract

Let $T$ be a multilinear Calderón-Zygmund operator of type $\omega$ with $\omega (t)$ being nondecreasing and satisfying a kind of Dini's type condition. Let $T_{\Pi \vec{b}}$ be the iterated commutators of $T$ with $BMO$ functions. The weighted strong and weak $L(\log L)$-type endpoint estimates for $T_{\Pi \vec{b}}$ with multiple weights are established. Some boundedness properties on weighted variable exponent Lebesgue spaces are also obtained. As applications, multiple weighted estimates for iterated commutators of paraproducts and bilinear pseudo-differential operators with mild regularity are given.