An endpoint weak-type estimate for multilinear Calderón-Zygmund operators (Q2326878)

The authors give a new proof of a weak-type \((1,\ldots,1;1/m)\) estimate for \(m\)-multilinear Calderón-Zygmund operators on \(\mathbb{R}^n\) proved first in [\textit{L. Grafakos} and \textit{R. H. Torres}, Adv. Math. 165, No. 1, 124--164 (2002; Zbl 1032.42020)]. The new proof uses a new weak-type estimate of the operators on a mixture of linear combinations of point mass measures and of \(L^1(\mathbb{R}^n)\cap L^{\infty}(\mathbb{R}^n)\) functions with appropriate \(L^{\infty}(\mathbb{R}^n)\) norms. A key result in the proofs is the authors' version of a multilinear geometric Hörmander regularity condition.