A new refinement of young's inequality

被引：8

作者：

Alzer, Horst ^{[1
]}

Koumandos, Stamatis ^{[1
]}

机构：

[1] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2007年 / 50卷

关键词：

trigonometric polynomials; sharp inequalities; Young's inequality; Fourier series;

D O I：

10.1017/S0013091504000744

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A classical theorem due to Young states that the cosine polynomial [Graphics] is positive for all n >= 1 and x epsilon (0, pi). We prove the following refinement. For all n >= 2 and x epsilon [0, pi] we have 1/6 + c(pi - X)(2) <= C-n (x), with the best possible constant factor [Graphics]

引用

页码：255 / 262

页数：8

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