Weighted weak-type bounds for multilinear singular integrals

We establish analogs of sharp weighted weak-type bounds for $m$-sublinear operators satisfying sparse form domination, including multilinear Calder\'on-Zygmund singular integrals. Our results, which hold for general $\vec{p} \in [1,\infty)^m$ and feature quantitative improvements, rely on new local testing conditions and good-$\lambda$ inequalities. We address weak-type bounds in both the change of measure and multiplier settings.