Geodesic
On discrete reversed Hardy–Littlewood–Sobolev inequalities
Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1025-1036

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DOI

Recently, the discrete reversed Hardy–Littlewood–Sobolev inequality with infinite terms was proved. In this article, we study the attainability of its best constant. For this purpose, we introduce a discrete reversed Hardy–Littlewood–Sobolev inequality with finite terms. The constraint of parameters of this inequality is more relaxed than that of parameters of inequality with infinite terms. We here show the limit relations between their best constants and between their extremal sequences. Based on these results, we obtain the attainability of the best constant of the inequality with infinite terms in the noncritical case.
DOI : 10.4153/S0008439525000293
Mots-clés : Discrete reversed Hardy–Littlewood–Sobolev inequality, best constant, attainability, extremal sequence 
Zhou, Tiantian; Lei, Yutian. On discrete reversed Hardy–Littlewood–Sobolev inequalities. Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1025-1036. doi: 10.4153/S0008439525000293
@article{10_4153_S0008439525000293,
     author = {Zhou, Tiantian and Lei, Yutian},
     title = {On discrete reversed {Hardy{\textendash}Littlewood{\textendash}Sobolev} inequalities},
     journal = {Canadian mathematical bulletin},
     pages = {1025--1036},
     year = {2025},
     volume = {68},
     number = {4},
     doi = {10.4153/S0008439525000293},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439525000293/}
}
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