A generalization of Hilbert's inequality

Peng Gao

doi:10.7153/mia-18-30

A generalization of Hilbert's inequality

Peng Gao^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	407-418
Number of pages	12
Journal	Mathematical Inequalities and Applications
Volume	18
Issue number	2
DOIs	https://doi.org/10.7153/mia-18-30
State	Published - 1 Apr 2015

Keywords

Hilbert's inequality

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10.7153/mia-18-30

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title = "A generalization of Hilbert's inequality",

abstract = "In a generalization of the classical Hilbert inequality by Hardy, Littlewood and P{\'o}lya, 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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AB - 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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DO - 10.7153/mia-18-30

M3 - 文章

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JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

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ER -

A generalization of Hilbert's inequality

Abstract

Keywords

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