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

## TL;DR

This paper presents two different proofs for a weighted weak-type estimate of multilinear Calderón-Zygmund operators, extending classical results to a multilinear and weighted setting.

## Contribution

It provides novel proofs for a weighted weak-type estimate of multilinear Calderón-Zygmund operators, inspired by classical and modern techniques.

## Key findings

- Two distinct proofs of the weighted weak-type estimate are provided.
- The proofs adapt classical Calderón-Zygmund decomposition and modern harmonic analysis ideas.
- The results extend classical weak-type estimates to multilinear and weighted contexts.

## Abstract

Two proofs of a weighted weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for multilinear Calder\'on-Zygmund operators are given. The ideas are motivated by different proofs of the classical weak-type $(1,1)$ estimate for Calder\'on-Zygmund operators. One proof uses the Calder\'on-Zygmund decomposition, and the other proof is motivated by ideas of Nazarov, Treil, and Volberg.