On the discrete Hardy inequality. (English) Zbl 0806.26011

Braverman, Michael Sh.; Stepanov, Vladimir D.

Bull. Lond. Math. Soc. 26, No. 3, 283-287 (1994).

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.

Reviewer: M.Sh.Braverman and V.D.Stepanov (Khabarovsk)

MSC:

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

Keywords:

discrete Hardy’s inequality; Halperin’s lemma; boundedness; discrete Hardy’s operator