Weak-Type Boundedness of the Hardy–Littlewood Maximal Operator on Weighted Lorentz Spaces - Agora, Elona (2016)
The main goal of this paper is to provide a characterization of the weak-type boundedness of the Hardy–Littlewood maximal operator, M, on weighted Lorentz spaces Λpᵤ(w), whenever p > 1. This solves a problem left open in (Carro et al., Mem Am Math Soc. 2007). 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.