Volume 4,  Issue 5, 2003

Article 94

ON HARDY-HILBERT'S INTEGRAL INEQUALITY WITH PARAMETERS

LEPING HE, MINGZHE GAO AND WEIJIAN JIA

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE,
NORMAL COLLEGE, JISHOU UNIVERSITY,
JISHOU HUNAN, 416000 
PEOPLE'S REPUBLIC OF CHINA.
E-Mail: lianheping@163.com

E-Mail: mingzhegao@163.com

E-Mail: jwj1959@163.com

Received 01 August, 2003; Accepted 28 August, 2003.
Communicated by: L. Debnath

ABSTRACT.   In this paper, by means of a sharpening of Hölder's inequality, Hardy-Hilbert's integral inequality with parameters is improved. Some new inequalities are established.
Key words:
Hardy-Hilbert integral inequality, Hölder's inequality, Weight function, Beta function.

2000 Mathematics Subject Classification:
26D15, 46C99.

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