Two-weight entropy Boundedness of Multilinear Fractional Type Operators

Abstract: 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.