Extensions of weak-type estimates for multilinear operators

Abstract

In this manuscript we extend the classical weighted weak-type inequalities from the bilinear to the multilinear setting. In particular, we develop a theory of restricted weak-type estimates for multilinear operators acting on various weighted function spaces. Our approach analyzes the sharpness and optimality of these bounds, establishes results under minimal kernel regularity assumptions, and extends the theory to non-classical function spaces such as variable exponent and Orlicz spaces. These advancements not only generalize known results but also provide new tools for applications in harmonic analysis and partial differential equations.