Acta mathematica scientia, Series B >
WEIGHTED NORM INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS
Received date: 2009-05-04
Revised date: 2010-03-25
Online published: 2011-05-20
Supported by
This research was supported by the NSFC (10971228).
In this paper, the authors consider the weighted estimates for the commutators of multilinear Calder\'on-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=∑1≤k≤m1/pk, then for any weight w, the commutators of m-linear Calder\'on-Zygmund operator are bounded from Lp1(Rn, ML(log L）σw)×Lp2(Rn, Mw)×…×Lpm(Rn, Mw) to Lp(Rn, w) with σ to be a constant depending only on p1 and the order of commutator.
HU Guo-En , ZHU Yue-Ping . WEIGHTED NORM INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS[J]. Acta mathematica scientia, Series B, 2011 , 31(3) : 749 -764 . DOI: 10.1016/S0252-9602(11)60273-7
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