International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 165089, 12 pages
doi:10.1155/2008/165089
On Hilbert's inequality for double series and its applications
Zhou Yu
and Gao Mingzhe
Department of Mathematics and Computer Science, Normal College of Jishou University, Jishou, Hunan 416000, China
Abstract
This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u(x) and a parameter λ. 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 in Hp function are given.