A generalization of Hilbert's inequality

2013/10/23 by Peng Gao, Gao, Peng
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematics and Applications #Matrix Theory and Algorithms #math.CA

paper · pdf · doi:10.48550/arxiv.1310.6106

9 pages

arxiv created 2013/10/23 · openalex publication_date 2013/10/23 · arxiv updated 2013/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a generalization of the classical Hilbert inequality by Hardy, Littlewood and Pólya, the best constant for an inequality is determined provided that the generating function for the corresponding matrix satisfies certain monotonicity condition. In this paper, we determine the best constant for a class of inequalities when the monotonicity condition is no longer satisfied.

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