Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Chen Xiaoyu, Gao Mingzhe and Ouyang Baiyu
Pages: [231] - [243]
Received Date: October 3, 2008
Submitted by: Themistocles M. Rassias
In this paper, a new refinement of the Hilbert inequality for double series can be established by means of Euler-Maclaurin summation and by introducing a proper weight function. A similar result for the Hilbert integral inequality is also proved. As applications, some strengthened results of the Hardy-Littlewood theorem and the Widder theorem are given.
Hilbert inequality, weight function, 
function, Euler-Maclaurin summation
formula, Cauchy-Schwarz inequality.
