## 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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