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.
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.
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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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