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. 
@article{EMJ_2019_10_1_a4,
     author = {A. Senouci and N. Azzouz},
     title = {Hardy type inequality with sharp constant for $0 < p < 1$},
     journal = {Eurasian mathematical journal},
     pages = {52--58},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2019_10_1_a4/}
}
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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/