On Hilbert's Inequality for Double Series and Its Applications. (31st March 2008)

• Record Type: Journal Article
• Authors: Yu, Zhou; Mingzhe, Gao
• Other Names: Qi Feng Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2008(2008)
• Publication Date: 2008-03-31
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2008/165089
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real functionu ( x ) and a parameterλ . In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality inH p function are given.