A Note on a Multilinear Local $Tb$ Theorem for Calder\'on-Zygmund Operators

TL;DR

This paper extends a local $Tb$ theorem to a full multilinear version for Calderón-Zygmund operators, broadening the theoretical framework for analyzing these operators in harmonic analysis.

Contribution

It introduces a comprehensive multilinear local $Tb$ theorem, advancing the understanding of Calderón-Zygmund operators beyond previous linear results.

Findings

Established a multilinear local $Tb$ theorem for Calderón-Zygmund operators

Extended previous linear results to multilinear setting

Provided theoretical foundation for future research in harmonic analysis

Abstract

In this short note, we extend a local $Tb$ theorem that was proved in \cite{GHO} to a full multilinear local $Tb$ theorem.