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Some Further Extensions of Hardy's Inequality

Published online by Cambridge University Press:  20 November 2018

Ling-Yau Chan*
Affiliation:
Dept. of Industrial EngineeringUniversity of Hong Kong
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Let p > l, r≠1, and let f(x) be a non-negative function defined in [0, ∞). The following inequality is due to G. H. Hardy [5, Ch. IX]:

1.1

where according as r>1 or r < l.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Boas, R. P. Jr, Some integral inequalities related to Hardy's inequality, J. Analyse Math. 23 (1970), 53-63.Google Scholar
2. Bradley, J. S., Hardy's inequalities with mixed norms, Canad. Math. Bull. 21 (4) (1978), 405-408.Google Scholar
3. Chan, L. Y., Some extensions of Hardy's inequality, Canad. Math. Bull. 22 (2) (1979), 165-169.Google Scholar
4. Copson, E. T., Some integral inequalities, Proc. Roy. Soc. Edinburgh 75A, 13 (1975), 157-164.Google Scholar
5. Hardy, G. H., Littlewood, J. E. and Polya, G., Inequalities, 2nd Ed., Cambridge, 1959 Google Scholar
6. Imoru, C. O., On some integral inequalities related to Hardy's, Canad. Math. Bull. 20 (3) (1977), 307-312.Google Scholar
7. Leindler, L., Generalization of inequalities of Hardy and Littlewood, Acta Sci. Math. 31 (1970), 279-285.Google Scholar
8. Németh, J., Generalizations of the Hardy-Littlewood inequality, Acta Sci. Math. 32 (1971), 295-299; “II”, ibid.35 (1973), 127-134.Google Scholar
9. Shum, D. T., On integral inequalities related to Hardy's, Canad. Math. Bull. 14 (1971), 225-230.Google Scholar
10. Zygmund, A., Trigonometric series, vol. I, 2nd éd., Cambridge, 1968.Google Scholar