$A_p$-$A_\infty$ estimates for general multilinear sparse operators

TL;DR

This paper establishes $A_p$-$A_ Infty$ estimates for multilinear dyadic positive operators, providing a unified approach that simplifies deriving estimates for various operators like multilinear square functions and Fourier multipliers.

Contribution

The paper introduces new $A_p$-$A_ Infty$ estimates for multilinear dyadic positive operators, enabling easier derivation for related operators.

Findings

Unified $A_p$-$A_ Infty$ estimates for multilinear operators

Simplified derivation of estimates for multilinear square functions

Facilitates estimates for multilinear Fourier multipliers

Abstract

In this paper, we study the $A_p$-$A_\infty$ estimates for a class of multilinear dyadic positive operators. As applications, the $A_p$-$A_\infty$ estimates for different operators e.g. multilinear square functions and multilinear Fourier multipliers can be deduced very easily.