International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 4, Pages 237-250

On Bicheng-Debnath's generalizations of Hardy's integral inequality

Aleksandra Čižmešija1 and Josip Pečarić2

1Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb 10000, Croatia
2Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, Zagreb 10000, Croatia

Received 15 September 2000

Copyright © 2001 Aleksandra Čižmešija and Josip Pečarić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider Hardy's integral inequality and we obtain some new generalizations of Bicheng-Debnath's recent results. We derive two distinguished classes of inequalities covering all admissible choices of parameter k from Hardy's original relation. Moreover, we prove the constant factors involved in the right-hand sides of some particular inequalities from both classes to be the best possible, that is, none of them can be replaced with a smaller constant.