Hardy–Littlewoodʼs inequalities, well known in the case of a probability measure, are extended to the case of a monotone (but not necessarily additive) set function, called a capacity. The upper inequality is established in the case of a capacity assumed to be continuous and submodular, the lower — under assumptions of continuity and supermodularity.
Sous des hypothèses appropriées, nous généralisons les inégalités de Hardy–Littlewood, bien connues dans le cas où lʼespace mesurable sous-jacent est muni dʼune probabilité, au cas dʼune fonction dʼensembles monotone, appelée capacité. Le résultat fait usage de la théorie de lʼintégration au sens de Choquet.
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@article{CRMATH_2013__351_1-2_73_0,
author = {Grigorova, Miryana},
title = {Hardy{\textendash}Littlewood's inequalities in the case of a capacity},
journal = {Comptes Rendus. Math\'ematique},
pages = {73--76},
publisher = {Elsevier},
volume = {351},
number = {1-2},
year = {2013},
doi = {10.1016/j.crma.2013.01.008},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2013.01.008/}
}
TY - JOUR AU - Grigorova, Miryana TI - Hardy–Littlewoodʼs inequalities in the case of a capacity JO - Comptes Rendus. Mathématique PY - 2013 SP - 73 EP - 76 VL - 351 IS - 1-2 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2013.01.008/ DO - 10.1016/j.crma.2013.01.008 LA - en ID - CRMATH_2013__351_1-2_73_0 ER -
%0 Journal Article %A Grigorova, Miryana %T Hardy–Littlewoodʼs inequalities in the case of a capacity %J Comptes Rendus. Mathématique %D 2013 %P 73-76 %V 351 %N 1-2 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2013.01.008/ %R 10.1016/j.crma.2013.01.008 %G en %F CRMATH_2013__351_1-2_73_0
Grigorova, Miryana. Hardy–Littlewoodʼs inequalities in the case of a capacity. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 73-76. doi : 10.1016/j.crma.2013.01.008. https://www.numdam.org/articles/10.1016/j.crma.2013.01.008/
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