Weighted endpoint estimates for commutators of multilinear fractional integral operators

Abstract

Let m be a positive integer, 0 < α < mn, \(\overrightarrow b \) = (b 1, …, b m ) ε BMOm. 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.