Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 18030, 14 pages

Weight characterizations for the discrete Hardy inequality with kernel

Christopher A. Okpoti, Lars-Erik Persson, and Anna Wedestig

Department of Mathematics, Luleå University of Technology, Luleå 971 87, Sweden

Received 16 August 2005; Accepted 17 August 2005

Copyright © 2006 Christopher A. Okpoti 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.


A discrete Hardy-type inequality (n=1(k=1ndn,kak)qun)1/qC(n=1anpvn)1/p is considered for a positive “kernel” d={dn,k}, n,k+, and pq. For kernels of product type some scales of weight characterizations of the inequality are proved with the corresponding estimates of the best constant C. A sufficient condition for the inequality to hold in the general case is proved and this condition is necessary in special cases. Moreover, some corresponding results for the case when {an}n=1 are replaced by the nonincreasing sequences {an*}n=1 are proved and discussed in the light of some other recent results of this type.