IJPAM: Volume 50, No. 4 (2009)

SOME REFINEMENTS OF HARDY'S INEQUALITY

Gong Yan$^1$, Gao Mingzhe$^2$
$^{1,2}$Department of Mathematics and Computer Science
Normal College
Jishou University
Jishou, Hunan, 416000, P.R. CHINA
$^{1}$e-mail: [email protected]
$^{2}$e-mail: [email protected]


Abstract.In this paper it is shown that the Hardy inequality for discrete form can be improved by means of a sharpening of Hölder's inequality. A similar result for the Hardy integral inequality is also proved. And the coefficient $\left(\frac{p}{p-1}\right)^p$ of the classical Hardy inequality is further discussed.

Received: February 20, 2008

AMS Subject Classification: 26D15

Key Words and Phrases: Hardy's inequality, Hölder's inequality, parametric variable vector, integration by parts

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 4