Sharp Weighted Estimates for Multilinear Commutators

Multilinear commutators with vector symbol =(b1,…,bm) defined by are considered, where K is a Calderón–Zygmund kernel. The following a priori estimates are proved for w ∈ A∞. For 0 < p < ∞, there exists a constant C such that and where and ML(log L)α is an Orlicz type maximal operator. This extends, with a different approach, classical results by Coifman. As a corollary, it is deduced that the operators are bounded on Lp(w) when w ∈ Ap, and that they satisfy corresponding weighted L(log L)1/r‐type estimates with w ∈ A1.