IJPAM: Volume 57, No. 4 (2009)

ON HILBERT TYPE INTEGRAL INEQUALITY
AND APPLICATIONS

Yu Zhou$^1$, Mingzhe Gao$^2$
$^{1,2}$Department of Mathematics and Computer Science
Normal College
Jishou University
Jishou, Hunan, 416000, P.R. CHINA
$^1$e-mail: yuzhou863@126.com
$^2$e-mail: mingzhegao@163.com


Abstract.In this paper it is shown that a new Hilbert type integral inequality can be established by introducing an integral kernel function of the form $\Big( {\ln \textstyle{{x -
\alpha } \over {y - \alpha }}} \Big)^{2n}$, where $\alpha \ge 0$. And the constant factor expressed by the Euler number and $\pi $ is proved to be the best possible. As applications, some equivalent forms are given.

Received: November 12, 2009

AMS Subject Classification: 26D15

Key Words and Phrases: Hilbert's integral inequality, integral kernel function, Euler number, weight function, the best constant

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 4