Two-weight inequalities for multilinear maximal functions in Orlicz spaces

TL;DR

This paper investigates two-weight inequalities for multilinear maximal functions within Orlicz spaces, providing characterizations and norm estimates for these operators to advance understanding of their boundedness properties.

Contribution

It introduces Sawyer-type characterizations and new norm estimates for multilinear fractional and weighted maximal functions in Orlicz spaces, extending prior results.

Findings

Established Sawyer-type characterizations for these operators

Derived new norm estimates between different Orlicz spaces

Enhanced understanding of two-weight inequalities in multilinear settings

Abstract

In this note, we provide various two-weight norm estimates of the multi-linear fractional maximal function and weighted maximal function between different Orlicz spaces. More precisely, we obtain Sawyer-type characterizations and norm estimates for these operators.