On two-weight norm estimates for multilinear fractional maximal function

TL;DR

This paper establishes two-weight norm estimates and Sawyer-type characterizations for the multilinear fractional maximal function in the upper triangle case, extending classical embedding techniques.

Contribution

It introduces new Sawyer-type characterizations and two-weight norm estimates for the multilinear fractional maximal function, utilizing an extended Carleson Embedding approach.

Findings

Derived Sawyer-type characterizations for the operator

Established two-weight norm estimates in the upper triangle case

Extended Carleson Embedding techniques for this context

Abstract

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.