Weak Type Boundedness of the Hardy Littlewood Maximal Operator on Weighted Lorentz Spaces

The main goal of this paper is to provide a complete characterization of the weak-type boundedness of the Hardy-Littlewood maximal operator, $M$, on weighted Lorentz spaces $\Lambda^p_u(w)$, whenever $p>1$. This solves a problem left open in \cite{crs:crs}. Moreover, with this result, we complete the program of unifying the study of the boundedness of $M$ on weighted Lebesgue spaces and classical Lorentz spaces, which was initiated in the aforementioned monograph.