Unifying Inequalities Of Hardy, Copson, And Others

Keywords

26D15

Abstract

In order to provide an alternative proof to an inequality of Hilbert, Hardy proved$$\sum_{n=0}^{\infty} \left((n+1)^{-1} \sum_{k=0}^{n}x_k\right)^p \leq\left(\frac{p}{p-1} \right)^p\sum_{n=0}^\infty x_n^p. $$∑n=0∞ (n+1)-1∑k=0nxkp≤pp-1p∑n=0∞xpn.This inequality and its relatives triggered research activity concerning norm inequalities including new inequalities by Copson and Levinson. In this paper, three theorems are established from which related inequalities of Hardy, Copson, and Levinson and various extensions are deduced as corollaries.

Publication Date

6-5-2015

Publication Title

Aequationes Mathematicae

Volume

89

Issue

3

Number of Pages

497-510

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00010-013-0230-x

Socpus ID

84930377369 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84930377369

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