Weight Characterizations for the Discrete Hardy Inequality with Kernel
نویسنده
چکیده
A discrete Hardy-type inequality ( ∑∞ n=1( ∑n k=1dn,kak)un) ≤ C( ∑∞ n=1 a p nvn) 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 {a∗n }n=1 are proved and discussed in the light of some other recent results of this type.
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