[Une inégalité intégrale de type Hilbert avec noyau mixte dépendant de plusieurs paramètres]
Dans ce texte, nous obtenons, sous deux formes équivalentes, une inégalité intégrale de type Hilbert, avec un noyau mixte dépendant de plusieurs paramètres. Nous utilisons à cette fin des fonctions poids, des techniques dʼanalyse réelle et les fonctions gamma dʼEuler et zéta de Riemann, afin dʼexpliciter le facteur constant (cʼest-à-dire ne dépendant que des paramètres), dont il est démontré quʼil est le meilleur possible. En choisissant des valeurs spéciales des paramètres, nous en déduisons quelques résultats significatifs.
In this paper, by means of the weight function and the technique of real analysis, and introducing the Γ-function and the Riemann ζ-function to jointly characterize the constant factor, a Hilbert-type integral inequality with the mixed kernel of multi-parameters and its equivalent form are given; their constant factors are proved to be the best possible. By selecting special parameter values, some meaningful results are obtained.
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@article{CRMATH_2013__351_15-16_605_0,
author = {Liu, Qiong and Sun, Wenbing},
title = {A {Hilbert-type} integral inequality with the mixed kernel of multi-parameters},
journal = {Comptes Rendus. Math\'ematique},
pages = {605--611},
publisher = {Elsevier},
volume = {351},
number = {15-16},
year = {2013},
doi = {10.1016/j.crma.2013.09.001},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2013.09.001/}
}
TY - JOUR AU - Liu, Qiong AU - Sun, Wenbing TI - A Hilbert-type integral inequality with the mixed kernel of multi-parameters JO - Comptes Rendus. Mathématique PY - 2013 SP - 605 EP - 611 VL - 351 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.09.001/ DO - 10.1016/j.crma.2013.09.001 LA - en ID - CRMATH_2013__351_15-16_605_0 ER -
%0 Journal Article %A Liu, Qiong %A Sun, Wenbing %T A Hilbert-type integral inequality with the mixed kernel of multi-parameters %J Comptes Rendus. Mathématique %D 2013 %P 605-611 %V 351 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.09.001/ %R 10.1016/j.crma.2013.09.001 %G en %F CRMATH_2013__351_15-16_605_0
Liu, Qiong; Sun, Wenbing. A Hilbert-type integral inequality with the mixed kernel of multi-parameters. Comptes Rendus. Mathématique, Tome 351 (2013) no. 15-16, pp. 605-611. doi : 10.1016/j.crma.2013.09.001. http://www.numdam.org/articles/10.1016/j.crma.2013.09.001/
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Cité par Sources :
☆ Fund Project National Natural Science Foundation of China (No. 11171280). Scientific support project of the Hunan Education Department (Nos. 10C1186, 11C1133).
