International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 27, Pages 1423-1427

On further strengthened Hardy-Hilbert's inequality

Lü Zhongxue1,2

1School of Science, Nanjing University of Science & Technology, Nanjing 210094, China
2Department of Basic Science of Technology College, Xuzhou Normal University, Jiangsu , Xuzhou 221011, China

Received 7 May 2002

Copyright © 2004 Lü Zhongxue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We obtain an inequality for the weight coefficient ω(q,n) (q>1, 1/q+1/q=1, n) in the form ω(q,n)=:m=1(1/(m+n))(n/m)1/q<π/sin(π/p)1/(2n1/p+(2/a)n1/q) where 0<a<147/45, as n3; 0<a<(1C)/(2C1), as n=1,2, and C is an Euler constant. We show a generalization and improvement of Hilbert's inequalities. The results of the paper by Yang and Debnath are improved.