# An endpoint weak-type estimate for multilinear Calder\'on-Zygmund operators

## TL;DR

This paper offers an alternative proof for a key weak-type estimate of multilinear Calderón-Zygmund operators, simplifying understanding and potentially broadening applicability in harmonic analysis.

## Contribution

It provides a new proof method for the weak-type estimate, inspired by nonhomogeneous harmonic analysis techniques, improving upon prior proofs by Grafakos and Torres.

## Key findings

- Alternative proof of weak-type estimate
- Simplifies understanding of multilinear operators
- Potentially broadens application scope

## Abstract

The purpose of this article is to provide an alternative proof of the weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for $m$-multilinear Calder\'on-Zygmund operators on $\mathbb{R}^n$ first proved by Grafakos and Torres. Subsequent proofs in the bilinear setting have been given by Maldonado and Naibo and also by P\'erez and Torres. The proof given here is motivated by the proof of the weak-type $(1,1)$ estimate for Calder\'on-Zygmund operators in the nonhomogeneous setting by Nazarov, Treil, and Volberg.