Weak-type boundedness of the Hardy-Littlewood maximal operator on weighted Lorentz spaces

Abstract

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)Λup(w) , whenever p>1p>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.