Geodesic
Hardy-type inequality for $0$ and hypodecreasing functions
Eurasian mathematical journal, Tome 1 (2010) no. 3, pp. 27-42.

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The notion of a hypodecreasing function is introduced. Some properties of hypodecreasing functions are proved and several examples are given. It is established that the Hardy-type inequality for $L_p$-spaces with $0$ is satisfied for some spaces of hypodecreasing functions. The obtained result is in a certain sense sharp. 
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V. I. Burenkov; A. Senouci; T. V. Tararykova. Hardy-type inequality for $0

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