Weighted estimates for maximal multilinear commutators

Abstract

AbstractLet 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 , rj ≥ 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)