Orlicz spaces for which the Hardy-Littlewood maximal operators is bounded.

Gallardo, Diego. "Orlicz spaces for which the Hardy-Littlewood maximal operators is bounded.." Publicacions Matemàtiques 32.2 (1988): 261-266. <http://eudml.org/doc/41058>.

@article{Gallardo1988,
abstract = {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&gt;0 ψ(2s) / ψ(s) &lt; ∞.},
author = {Gallardo, Diego},
journal = {Publicacions Matemàtiques},
keywords = {Espacio de Orlicz; Operador maximal de Hardy-Littlewood; Operadores acotados; Hardy-Littlewood maximal operator; Orlicz spaces; boundedness},
language = {eng},
number = {2},
pages = {261-266},
title = {Orlicz spaces for which the Hardy-Littlewood maximal operators is bounded.},
url = {http://eudml.org/doc/41058},
volume = {32},
year = {1988},
}

TY - JOUR
AU - Gallardo, Diego
TI - Orlicz spaces for which the Hardy-Littlewood maximal operators is bounded.
JO - Publicacions Matemàtiques
PY - 1988
VL - 32
IS - 2
SP - 261
EP - 266
AB - 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&gt;0 ψ(2s) / ψ(s) &lt; ∞.
LA - eng
KW - Espacio de Orlicz; Operador maximal de Hardy-Littlewood; Operadores acotados; Hardy-Littlewood maximal operator; Orlicz spaces; boundedness
UR - http://eudml.org/doc/41058
ER -