Original Article
Kyungpook Mathematical Journal 2008; 48(3): 457-463
Published online September 23, 2008
Copyright © Kyungpook Mathematical Journal.
On Certain Extension of Hilbert’s Integral Inequality with Best Constants
Yongjin Li1, Yu Lin2, Bing He3
1Institute of Logic and Cognition, Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China
2Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China
3Department of Mathematics, Guangdong Education College, Guangzhou, 510303, China
In this paper, by introducing a new function with two parameters, we give another generalizations of the Hilbert's integral inequality with a mixed kernel $k(x, y) = frac{1}{A(x + y) + B |x - y|}$ and a best constant factors. As applications, some particular results with the best constant factors are considered.
Keywords: Hilbert's integral inequality, Weight function