A New Proof of the Boundedness of Maximal Operators on Variable Lebesgue Spaces
Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 1, pp. 151-173
Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica
We give a new proof using the classic Calderón-Zygmund decomposition that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue space $L^{p(\cdot)}$ whenever the exponent function $p(\cdot)$ satisfies log-Hölder continuity conditions. We include the case where $p(\cdot)$ assumes the value infinity. The same proof also shows that the fractional maximal operator $M_{a}$, $0 a n$, maps $L^{p(\cdot)}$ into $L^{q(\cdot)}$, where $1/p(\cdot) - 1/q(\cdot) = a/n$.
@article{BUMI_2009_9_2_1_a7,
author = {Cruz-Uribe, D. and Diening, L. and Fiorenza, A.},
title = {A {New} {Proof} of the {Boundedness} of {Maximal} {Operators} on {Variable} {Lebesgue} {Spaces}},
journal = {Bollettino della Unione matematica italiana},
pages = {151--173},
publisher = {mathdoc},
volume = {Ser. 9, 2},
number = {1},
year = {2009},
zbl = {1207.42011},
mrnumber = {2493649},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_1_a7/}
}
TY - JOUR AU - Cruz-Uribe, D. AU - Diening, L. AU - Fiorenza, A. TI - A New Proof of the Boundedness of Maximal Operators on Variable Lebesgue Spaces JO - Bollettino della Unione matematica italiana PY - 2009 SP - 151 EP - 173 VL - 2 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_1_a7/ LA - en ID - BUMI_2009_9_2_1_a7 ER -
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Cruz-Uribe, D.; Diening, L.; Fiorenza, A. A New Proof of the Boundedness of Maximal Operators on Variable Lebesgue Spaces. Bollettino della Unione matematica italiana, Série 9, Tome 2 (2009) no. 1, pp. 151-173. http://geodesic.mathdoc.fr/item/BUMI_2009_9_2_1_a7/