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Science China Mathematics

, Volume 56, Issue 9, pp 1879–1894 | Cite as

Multiple weighted estimates for commutators of multilinear fractional integral operators

  • SongQing Chen
  • HuoXiong Wu
Articles

Abstract

Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.

Keywords

multilinear fractional integrals commutators maximal operators multiple weights \(A\left( {\vec P,q} \right)\) weighted norm inequalities 

MSC(2010)

42B20 42B25 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamenChina
  2. 2.School of EconomicsShanghai University of Finance and EconomicsShanghaiChina

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