Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-19T21:50:57.360Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Further Extensions of Hardy's Inequality

Published online by Cambridge University Press:  20 November 2018

Ling-Yau Chan
Ling-Yau Chan*
Affiliation:
Dept. of Industrial EngineeringUniversity of Hong Kong
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 393 - 400
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