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A Hardy-Hilbert’s type inequality with gamma function and its applications. (English) Zbl 1105.26014

By using the \(\Gamma\) function and estimating the weight function, the authors give a new Hardy-Hilbert’s type integral inequality. And the double series analogue is considered. As applications, some extensions of Hardy-Littlewood’s theorem are given.

MSC:

26D15 Inequalities for sums, series and integrals
33B15 Gamma, beta and polygamma functions
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References:

[1] Hardy G. H., Inequalities (1952)
[2] Mitrinovic D. S., Inequalities Involving Functions and Their Integral and Derivatives (1991)
[3] Yang Bicheng, Journal of Mathematical Analysis and Applications 272 pp 187– (2002) · Zbl 1009.26016 · doi:10.1016/S0022-247X(02)00151-8
[4] Yang Bicheng, Chinese Quarterly Journal of Mathematics 13 pp 83– (1998)
[5] Yang Bicheng, Journal of Mathematical Analysis and Applications 220 pp 778– (1998) · Zbl 0911.26011 · doi:10.1006/jmaa.1997.5877
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[7] Yang Bicheng, Chinese Annals of Mathematics (Series A) 21 pp 401– (2000)
[8] Wang Zhuqi, An Introduction to Special Functions (1979)
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