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Weighted norm inequalities for the commutators of multilinear singular integral operators
Authors:Guoen Hu  Yueping Zhu  
Institution:a Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China;b School of Science, Nantong University, Nantong 226007, China
Abstract: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.
Keywords:multilinear Calderó  n-Zygmund operator  weighted norm inequality  commutator  Calderó  n-Zygmund decomposition2000 MR Subject Classification: 42B20
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