Journal of Inequalities and Applications
Volume 1 (1997), Issue 1, Pages 25-46

On some fractional order hardy inequalities

Hans P. Heinig,1 Alois Kufner,2 and Lars-Erik Persson3

1Department of Mathematics & Statistics, McMaster University, Ontario, Hamilton L8S 4K1, Canada
2Mathematical Institute, Czech Academy of Sciences, Žitná 25, Praha 1 115 67, Czech Republic
3Department of Mathematics, Luleå University, Luleå S-971 87, Sweden

Received 6 May 1996

Copyright © 1997 Hans P. Heinig et al. 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.


Weighted inequalities for fractional derivatives (= fractional order Hardy-type inequalities) have recently been proved in [4] and [1]. In this paper, new inequalities of this type are proved and applied. In particular, the general mixed norm case and a general twodimensional weight are considered. Moreover, an Orlicz norm version and a multidimensional fractional order Hardy inequality are proved. The connections to related results are pointed out.