On discrete reversed Hardy–Littlewood–Sobolev inequalities

Abstract 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.