scholarly journals Multiple Weighted Estimates for Vector-Valued Multilinear Singular Integrals with Non-Smooth Kernels and Its Commutators

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Dongxiang Chen ◽  
Dan Zou ◽  
Suzhen Mao
Keyword(s):  
Singular Integrals ◽  
Weighted Norm ◽  
Multilinear Commutator ◽  
Weighted Estimates ◽  
Bmo Functions ◽  
Multilinear Singular Integral Operator ◽  
Smooth Kernels ◽  
New Variant ◽  
Vector Valued ◽  
Multilinear Singular Integrals

This note concerns multiple weighted inequalities for vector-valued multilinear singular integral operator with nonsmooth kernel and its corresponding commutators containing multilinear commutator and iterated commutator generated by the vector-valued multilinear operator and BMO functions. By the weighted estimates for a class of new variant maximal and sharp maximal functions, the multiple weighted norm inequalities for such operators are obtained.

scholarly journals Weighted Estimates for Maximal Commutators of Multilinear Singular Integrals

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Dongxiang Chen ◽  
Suzhen Mao
Keyword(s):  
Linear Operator ◽  
Lipschitz Function ◽  
Singular Integrals ◽  
Pointwise Estimates ◽  
Multilinear Commutator ◽  
Weighted Lipschitz Function ◽  
Weighted Estimates ◽  
Sharp Function ◽  
Multilinear Commutators ◽  
Multilinear Singular Integrals

This paper is concerned with the pointwise estimates for the sharp function of the maximal multilinear commutatorsTΣb*and maximal iterated commutatorTΠb*, generalized bym-linear operatorTand a weighted Lipschitz functionb. The(Lp1(μ)×⋯×Lpm(μ),Lr(μ1-r))boundedness and the(Lp1(μ)×⋯×Lpm(μ),Lr(μ1-mr))boundedness are obtained for maximal multilinear commutatorTΣb*and maximal iterated commutatorTΠb*, respectively.

scholarly journals Multiple-weighted norm inequalities for maximal multi-linear singular integrals with non-smooth kernels

2011 ◽  
Vol 141 (4) ◽  
pp. 755-775 ◽  
Author(s):  
Loukas Grafakos ◽  
Liguang Liu ◽  
Dachun Yang
Keyword(s):  
Singular Integrals ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Weighted Estimates ◽  
New Class ◽  
Littlewood Maximal Function ◽  
Smooth Kernels ◽  
Multiple Weights

We obtain weighted norm inequalities for maximal truncated operators of multi-linear singular integrals with non-smooth kernels in the sense of Duong et al. This class of operators extends the class of multi-linear Calderón-Zygmund operators introduced by Coifman and Meyer and includes the higher-order commutators of Calderón. The weighted norm inequalities obtained in this work are with respect to the new class of multiple weights of Lerner et al. The key ingredient in the proof is the introduction of a new multi-sublinear maximal operator that plays the role of the Hardy-Littlewood maximal function in a version of Cotlar's inequality. As applications of these results, new weighted estimates for the mth order Calderón commutators and their maximal counterparts are deduced.

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