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Keywords:
multilinear fractional integral operators; commutator; BMO; weight; maximal operators
Summary:
Let $m$ be a positive integer, $0<\alpha <mn$, $\vec {b}=(b_{1},\cdots ,b_{m})\in {\rm BMO}^m$. We give sufficient conditions on weights for the commutators of multilinear fractional integral operators $\Cal {I}^{\vec {b}}_{\alpha }$ 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.
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