Probability Theory
Hardy–Littlewoodʼs inequalities in the case of a capacity
Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 73-76.

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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DOI: 10.1016/j.crma.2013.01.008
Grigorova, Miryana 1

1 LPMA, CNRS–UMR 7599, université Denis-Diderot – Paris-7, 175, rue du Chevaleret, 75013 Paris, France
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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. http://www.numdam.org/articles/10.1016/j.crma.2013.01.008/

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