ON A MAXIMAL OPERATOR IN REARRANGEMENT INVARIANT BANACH FUNCTION SPACES ON METRIC SPACES

Abstract

We introduce a maximal operator for functions defined on a doubling metric measure space, belonging to a rearrangement Banach function space. We provide some estimates for the distribution function of this operator, generalizing results proved by Bastero, Mil-man and Ruiz (1999) in the Euclidean case and by Costea and Miranda (2012) for New-tonian Lorentz spaces on metric spaces.

Cuvinte cheie

metric measure space rearrangement invariant Banach function space (Hardy-Littlewood) maximal operator