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Czechoslovak Mathematical Journal

, Volume 62, Issue 2, pp 347–359 | Cite as

Weighted endpoint estimates for commutators of multilinear fractional integral operators

  • Xuefang Yan
  • Limei Xue
  • Wenming Li
Article

Abstract

Let m be a positive integer, 0 < α < mn, \(\overrightarrow b \) = (b 1, …, b m ) ε BMO m . We give sufficient conditions on weights for the commutators of multilinear fractional integral operators \({\rm I}_a^{\overrightarrow b }\) to satisfy a weighted endpoint inequality which extends the result in D. Cruz-Uribe, A. Fiorenza: Weighted endpoint estimates for commutators of fractional integrals, Czech. Math. J. 57 (2007), 153–160. We also give a weighted strong type inequality which improves the result in X. Chen, Q. Xue: Weighted estimates for a class of multilinear fractional type operators, J. Math. Anal. Appl., 362, (2010), 355–373.

Keywords

multilinear fractional integral operators commutator BMO weight maximal operators 

MSC 2010

42B20 42B25 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2012

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceHebei Normal UniversityShijiazhuangP.R.China

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