数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 749-764.doi: 10.1016/S0252-9602(11)60273-7

• 论文 •    下一篇

WEIGHTED NORM INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS

胡国恩|朱月萍   

  1. Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China; School of Science, Nantong University, Nantong 226007, China
  • 收稿日期:2009-05-04 修回日期:2010-03-25 出版日期:2011-05-20 发布日期:2011-05-20
  • 通讯作者: 朱月萍 E-mail:guoenxx@yahoo.com.cn;zhuyueping@ntu.edu.cn
  • 基金资助:

    This research was supported by the NSFC (10971228).

WEIGHTED NORM INEQUALITIES FOR THE COMMUTATORS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS

 HU Guo-En, ZHU Yue-Ping   

  1. Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China; School of Science, Nantong University, Nantong 226007, China
  • Received:2009-05-04 Revised:2010-03-25 Online:2011-05-20 Published:2011-05-20
  • Contact: Zhu Yueping E-mail:guoenxx@yahoo.com.cn;zhuyueping@ntu.edu.cn
  • Supported by:

    This research was supported by the NSFC (10971228).

摘要:

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 p∈ (1, ∞), p2, … , pm ∈ (1, ∞], ∈(0, ∞) with 1/p=∑1≤km1/pk, then  for any weight w, the commutators of m-linear Calder\'on-Zygmund operator are bounded from Lp1(Rn, ML(log LσwLp2(Rn, Mw)×…×Lpm(Rn, Mw) to Lp(Rn, w)  with σ to be a constant depending only on p1 and the order of commutator.

关键词: multilinear Calderon-Zygmund operator, weighted norm inequality, commutator, Calderon-Zygmund decomposition

Abstract:

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 p∈ (1, ∞), p2, … , pm ∈ (1, ∞], ∈(0, ∞) with 1/p=∑1≤km1/pk, then  for any weight w, the commutators of m-linear Calder\'on-Zygmund operator are bounded from Lp1(Rn, ML(log LσwLp2(Rn, Mw)×…×Lpm(Rn, Mw) to Lp(Rn, w)  with σ to be a constant depending only on p1 and the order of commutator.

Key words: multilinear Calderon-Zygmund operator, weighted norm inequality, commutator, Calderon-Zygmund decomposition

中图分类号: 

  • 42B20