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On Hardy–Hilbert's Integral Inequality

✍ Scribed by Yang Bicheng

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
103 KB
Volume
261
Category
Article
ISSN
0022-247X

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This paper deals with some new generalizations of Hardy's integral inequality. An improvement of some inequality is also presented.

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In this note, it is shown that the Hardy᎐Hilbert inequality for double series can Ž . be improved by introducing a proper weight function of the form rsin rp y Ž . 1y1rr Ž Ž . . O n rn with O n ) 0 into either of the two single summations. When r r r s 2, the classical Hilbert inequality is improved