Sharp weighted estimates for multi-linear Calder\'{o}n-Zygmund operators on non-homogeneous spaces

TL;DR

This paper establishes sharp weighted bounds for multilinear Calderón-Zygmund operators on non-homogeneous metric spaces using sparse domination techniques, advancing the understanding of their behavior in complex measure spaces.

Contribution

It introduces pointwise sparse domination results for multilinear Calderón-Zygmund operators on non-homogeneous spaces, leading to sharp weighted estimates.

Findings

Established pointwise sparse domination for multilinear operators

Derived sharp quantitative weighted estimates

Extended results to non-homogeneous metric measure spaces

Abstract

In this article, we address pointwise sparse domination for multilinear Calder\'on-Zygmund operators on upper doubling, geometrically doubling metric measure spaces. As a consequence, we have obtained sharp quantitative weighted estimates for multilinear Calder\'on-Zygmund operators.