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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Miryana Grigorova 1
@article{CRMATH_2013__351_1-2_73_0, author = {Miryana Grigorova}, 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}, }
Miryana Grigorova. 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://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.01.008/
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