Weighted estimates for a class of multilinear fractional type operators

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Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators (2011, methodology): “7) has already been obtained in [4], Proposition 5.”
Weighted inequalities for multilinear fractional integral operators (2009, methodology): “We not only prove sufficiency but also the necessity of the condition and our methods of proof are different from those in [2] and [5].”
Compactness properties of commutators of bilinear fractional integrals (2013, result): “bkBMOkfkLp kgkLq. As usual, the notation x . y indicates that x ≤ Cy with a positive constant C independent of x and y. For a proof of the above boundedness properties, see the papers by Chen and Xue [7] and Lian and Wu [18]. In the linear case the corresponding result goes back to the work of Chani”