no. 1-2
Probability Theory
Hardy–Littlewoodʼs inequalities in the case of a capacity
[Inégalités de Hardy–Littlewood dans le cas dʼune capacité]
Présenté par : the Editorial Board
Grigorova, Miryana1
1 LPMA, CNRS–UMR 7599, université Denis-Diderot – Paris-7, 175, rue du Chevaleret, 75013 Paris, France
Comptes Rendus. Mathématique, Tome 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.

Reçu le :
Accepté le :
Publié le :
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 
@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},
     year = {2013},
     publisher = {Elsevier},
     volume = {351},
     number = {1-2},
     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, Tome 351 (2013) no. 1-2, pp. 73-76. doi: 10.1016/j.crma.2013.01.008

[1] Denneberg, D. Non-Additive Measure and Integral, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994

[2] Föllmer, H.; Schied, A. Stochastic Finance. An Introduction in Discrete Time, De Gruyter Studies in Mathematics, 2004

[3] M. Grigorova, Stochastic orderings with respect to a capacity and an application to a financial optimization problem, Working paper, hal-00614716, 2011.

[4] M. Grigorova, Stochastic dominance with respect to a capacity and risk measures, Working paper, hal-00639667, 2011.

Cité par Sources :