We prove some Sawyer-type characterizations for multilinear fractional maximal function for the upper triangle case. We also provide some two-weight norm estimates for this operator. As one of the main tools, we use an extension of the usual Carleson Embedding that is an analogue of the P. L. Duren extension of the Carleson Embedding for measures.
Benoît Florent SEHBA. "On two-weight norm estimates for multilinear fractional maximal function." J. Math. Soc. Japan 70 (1) 71 - 94, January, 2018. https://doi.org/10.2969/jmsj/07017358