IJPAM: Volume 57, No. 4 (2009)
Department of Mathematics and Computer Science
Jishou, Hunan, 416000, P.R. CHINA
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 , where . And the constant factor expressed by the Euler number and 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