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On discrete reversed Hardy–Littlewood–Sobolev inequalities

Part of: Functional analytic methods in summability Inequalities

Published online by Cambridge University Press:  14 March 2025

Tiantian Zhou  and
Yutian Lei
Tiantian Zhou
Affiliation:
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China e-mail: ztt0515@foxmail.com
Yutian Lei*
Affiliation:
Ministry of Education Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China
*
e-mail: leiyutian@njnu.edu.cn
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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.

Keywords

Discrete reversed Hardy–Littlewood–Sobolev inequalitybest constantattainabilityextremal sequence

MSC classification

Primary: 40H05: Functional analytic methods in summability
Secondary: 26D15: Inequalities for sums, series and integrals 40B05: Multiple sequences and series (should also be assigned at least one other classification number in this section)

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Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 12
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This research was supported by the Natural Science Foundation of Jiangsu (No. BK20241878) and Postgraduate Research and Practice Innovation Program of Jiangsu Province (No. KYCX24-1791).

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