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

Abstract

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 ${\Lambda }_u^p(w)$, 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.

arXiv comment7 pages

References in corpus (1)

• Lorentz-Shimogaki and Boyd theorems for weighted Lorentz spaces