# IJPAM: Volume 19, No. 2 (2005)

A HARDY-HILBERT'S TYPE INTEGRAL
INEQUALITY WITH WEIGHTS AND
ITS APPLICATION

Yang Qiaoshun, Gao Mingzhe
Department of Mathematics and Computer Science
Normal College
Jishou University
Jishou Hunan, 416 000, P.R. CHINA
e-mail: yqs244@163.com
e-mail: mingzhegao@163.com

Abstract.In this paper, it is shown that a Hardy-Hilbert's type integral inequality with weights can be established by introducing a power-exponent function of the form , and the coefficient is proved to be best possible. In particular, for case , some extensions of the classical Hilbert integral inequality are obtained. As application, some generalizations of Hardy-Littlewood's integral inequality are given.