Journal of Inequalities and Applications 
Volume 1 (1997), Issue 1, Pages 25-46
doi:10.1155/S1025583497000039

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

Abstract

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.