IJPAM: Volume 72, No. 3 (2011)

AN EXTENDED HARDY-HILBERT TYPE INEQUALITY
WITH WEIGHTS AND ITS APPLICATIONS

Qiaoshun Yang$^1$, Zhiting Xu$^2$, Ping Long$^3$
$^{1,3}$Department of Mathematics and Computer Science
Normal College
Jishou University
Jishou Hunan , 416000, P.R. CHINA
$^2$School of Mathematical Sciences
South China Normal University
Guangzhou, 510631, P.R. CHINA


Abstract. By introducing a power-exponent function with the form $ax^{\alpha + \beta x}+by^{\alpha + \beta y}$ and two pairs of conjugate exponents, an extended Hardy-Hilbert's integral inequality was established. As applications, some extensions of Hardy-Littlewood's integral inequality are also given.

Received: October 7, 2010

AMS Subject Classification: 26D15

Key Words and Phrases: Power-exponent function, weight function, integral inequality, conjugate exponent

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 3