Let M be the Hardy-Littlewood maximal operator defined by:
Mf(x) = supx ∈ Q 1/|Q| ∫Q |f| dx, (f ∈ Lloc(Rn)),
where the supreme is taken over all cubes Q containing x and |Q| is the Lebesgue measure of Q. In this paper we characterize the Orlicz spaces Lφ*, associated to N-functions φ, such that M is bounded in Lφ*. We prove that this boundedness is equivalent to the complementary N-function ψ of φ satisfying the Δ2-condition in [0,∞), that is, sups>0 ψ(2s) / ψ(s) < ∞.
@article{urn:eudml:doc:41058,
title = {Orlicz spaces for which the Hardy-Littlewood maximal operators is bounded.},
journal = {Publicacions Matem\`atiques},
volume = {32},
year = {1988},
pages = {261-266},
mrnumber = {MR0975900},
zbl = {0685.46016},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41058}
}
Gallardo, Diego. Orlicz spaces for which the Hardy-Littlewood maximal operators is bounded.. Publicacions Matemàtiques, Tome 32 (1988) pp. 261-266. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41058/