ON A MAXIMAL OPERATOR IN REARRANGEMENT INVARIANT BANACH FUNCTION SPACES ON METRIC SPACES
MARCELINA MOCANU
Department of Mathematics, Informatics and Education Sciences, Faculty of Sciences, "Vasile Alecsandri" University of Bacău, 157 Calea Mărăşeşti, 600115 Bacău, ROMANIA, e-mail: mmocanu@ub.ro
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.