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

Two proofs of a weighted weak-type $(1,\dots ,1;\frac{1}{m})$ 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.