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

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.