IUMJ

Title: The Hardy-Littlewood maximal type operators between Banach function spaces

Authors: Mieczyslaw Mastylo and Carlos Perez

Issue: Volume 61 (2012), Issue 3, 883-900

Abstract:

We investigate variants of the maximal operator and show their applications to study boundedness of the classical Hardy-Littlewood maximal operator between weighted Banach function spaces which satisfy certain geometrical lattice conditions. We prove inequalities for rearrangement of the maximal operators generated by rearrangement invariant spaces. Applying this to the Lorentz spaces, we give new sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted $L^p$-spaces with different weights. We also prove that under some mild hypotheses these conditions are also necessary.