WEIGHTED NORM INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS

In this paper, the authors consider the weighted estimates for the commutators of multilinear Calderón-Zygmund operators.By introducing an operator which shifts the commutation, and establishing the weighted estimates for this new operator, the authors prove that, if p1 ∈ （1,∞）, p2,…,pm ∈(1,∞], p ∈ （0,∞） with 1/p =Σ1≤k≤ m 1/pk, then for any weight w, the commutators of m-linear Galderón-Zygmund operator are bounded from LP1（Rn,Ml（logL）σw）× p2（Rn,Mw）×...×Lpm（Rn,Mw） to Lp（Rn,w）with σ to be a constant depending only on p1 and the order of commutator