An Endpoint Weak-Type Estimate for Multilinear Calderón–Zygmund Operators

The purpose of this article is to provide an alternative proof of the weak-type 1,…,1;1m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( 1,\ldots ,1;\frac{1}{m}\right) $$\end{document} estimate for m-multilinear Calderón–Zygmund operators on Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^n$$\end{document} first proved by Grafakos and Torres. Subsequent proofs in the bilinear setting have been given by Maldonado and Naibo and also by Pérez and Torres. The proof given here is motivated by the proof of the weak-type (1, 1) estimate for Calderón–Zygmund operators in the nonhomogeneous setting by Nazarov, Treil, and Volberg.