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On the discrete Hardy inequality. (English) Zbl 0806.26011

Necessary and sufficient conditions for the boundedness of the discrete Hardy’s operator of the form \(Pf(n)= \sum^ n_{k=1} f(k)\), from \(l^ p_ v\) to \(l^ q_ u\) when \(0< q< 1< p<\infty\) is given.

MSC:

26D15 Inequalities for sums, series and integrals
42B25 Maximal functions, Littlewood-Paley theory
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