Geodesic
Hardy type inequality with sharp constant for $0 p 1$
Eurasian mathematical journal, Tome 10 (2019) no. 1, pp. 52-58.

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A power-weighted integral inequality with sharp constant for $0 p 1$ was established by V.I. Burenkov for the Hardy operator $(Hf)(x)=\frac1x\int_0^xf(t)\,dt$ for non-negative non-increasing functions $f$. In this work we consider a more general class of functions $f$ and prove a new Hardy-type inequality with sharp constant for functions of this class. 
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A. Senouci; N. Azzouz. Hardy type inequality with sharp constant for $0 < p < 1$. Eurasian mathematical journal, Tome 10 (2019) no. 1, pp. 52-58. http://geodesic.mathdoc.fr/item/EMJ_2019_10_1_a4/

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