Quantitative weighted estimates for generalized commutators of multilinear Calderón–Zygmund operators with the kernels of Dini type

Let T be a multilinear Calderón–Zygmund operator of type \(\omega \). \(T_{\vec {b},S}\) is the generalized commutator of T, which generalizes several commutators that already existed. It is shown in this paper that the weak and strong type quantitative weighted estimates for \(T_{\vec {b},S}\) when \(\vec {b}=\{b_i\}_{i=1}^{\infty }\) belongs to exponential oscillation spaces and Lipschitz spaces, respectively. As applications, we obtain the multiple weighted norm inequalities for the generalized commutators of bilinear pseudo-differential operators and paraproducts with mild regularity.