Weighted estimates for maximal multilinear commutators

Abstract Let T be a Calderón–Zygmund operator with regular kernel K and T * b be the maximal multilinear commutator defined by equation image . In this paper, the following weighted estimates for T * b are discussed. Precisely, for 0 < p < ∞, ω ∈ A ∞ and b j ∈ Osc , r j ≥ 1, j = 1, … , m , there exists a positive constant C such that equation image . For p = 1 and ω ∈ A 1 , the weighted weak L (log L ) 1/ r ‐type estimates are also established. Our theorems are parallel to the ones of the multilinear commutators of Calderón–Zygmund operators obtained in [18] and extend the main result in [14] essentially. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)