Two-weight entropy Boundedness of Multilinear Fractional Type Operators
  This paper will be devoted to study the two-weight norm inequalities of the multilinear fractional maximal operator $\mathcal{M}_{\alpha}$ and the multilinear fractional integral operator $\mathcal{I}_{\alpha}$. The entropy conditions in the multilinear setting will be introduced and the entropy bounds for $\mathcal{M}_\alpha$ and $\mathcal{I}_\alpha$ will be given. 
Mingming Cao and Qingying Xue
math.CA