Geodesic
On Integral Inequalities Related to Hardy's
Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 225-230

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this note is to provide integral inequalities which are related to Hardy's ([2] and [3, Theorem 330]). This latter result we state asTheorem 1. Let p>1, r≠1, and ƒ(x) be nonnegative and Lebesgue integrable on [0, a] or [a, ∞] for every a>0, according as r> 1 or r< 1. If F(x) is defined by 1 then 2 unless f≡0. The constant is the best possible. 
Shum, D. T. On Integral Inequalities Related to Hardy's. Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 225-230. doi: 10.4153/CMB-1971-038-4
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[1] 1. Benson, D. C., Inequalities involving integrals of functions and their derivatives, J. Math. Anal. Appl. 17 (1967), 292-308. Google Scholar

[2] 2. Hardy, G. H., Note on some points in the integral calculus (LXIV), Messenger of Math. 57 (1928), 12-16. Google Scholar

[3] 3. Hardy, G. H., Littlewood, J. E., and Pólya, G., Inequalities, second edition, Cambridge, 1952. Google Scholar

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