Weight characterizations for the discrete Hardy inequality with kernel

A discrete Hardy-type inequality (∑n=1∞(∑k=1ndn,kak)qun)1/q≤C(∑n=1∞anpvn)1/p is considered for a positive "kernel" d={dn,k}, n,k∈ℤ+, and p≤q. 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.Validerad; 2006; Bibliografisk uppgift: Paper id:: 18030; 20070111 (evan)