Christopher Adjei Okpoti

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Scales of equivalent weight characterizations for the Hardy type inequality with general measures are proved. The conditions are valid in the case of indices 0 < q < p <∞, p > 1. We also include a reduction theorem for transferring a three-measure Hardy inequality to the case with two measures. © 2007 Elsevier Inc. All rights reserved.
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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(More)
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