V. I. Burenkov, A. Senouci, T. V. Tararykova, “Hardy-type inequality for <nobr>$0<p<1$</nobr> and hypodecreasing functions”, Eurasian Math. J., 2010, Volume 1, Number 3,Pages <nobr>27

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Hardy-type inequality for $0<p<1$ and hypodecreasing functions

V. I. Burenkov^a, A. Senouci^b, T. V. Tararykova^a

^a Faculty of Mechanics and Mathematics L. N. Gumilyov Eurasian National University, Astana, Kazakhstan
^b Department of Mathematics Ibnou-Khaldoun University, Tiaret, Algeria

Abstract: 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 $0<p<1$ is satisfied for some spaces of hypodecreasing functions. The obtained result is in a certain sense sharp.

Keywords and phrases: the Hardy inequality, $L_p$-spaces with $0<p<1$, hypodecreasing functions.

MSC: 47B38

Received: 12.07.2010

Language: English