A strengthening of the Carleman-Hardy-Pólya inequality期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A strengthening of the Carleman-Hardy-Pólya inequality

Authors:	Finbarr Holland

Affiliation:	Mathematics Department, University College, Cork, Ireland

Abstract:	As a consequence of a more general statement proved in the paper, it is deduced that, if , and , then $displaystyle left(frac{sum_{j=1}^n root jof{a_1a_2dotsm a_j}}{sum_{j=1}... ...of{a_1a_2dotsm a_n}}{sum_{j=1}^n root jof{a_1a_2dotsm a_j}}lefrac{n+1}n,$ with equality if and only if . This is a new refinement of Carleman's classic inequality.

Keywords:	Weighted geometric means Carleman's inequality convex functions

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