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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@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 = {http://archive.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 - http://archive.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 http://archive.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, Tome 351 (2013) no. 1-2, pp. 73-76. doi : 10.1016/j.crma.2013.01.008. http://archive.numdam.org/articles/10.1016/j.crma.2013.01.008/
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