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Eurasian Math. J., 2010, Volume 1, Number 3, Pages 27–42 (Mi emj27)  

This article is cited in 3 scientific papers (total in 3 papers)

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

V. I. Burenkova, A. Senoucib, T. V. Tararykovaa

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.

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Document Type: Article
MSC: 47B38
Received: 12.07.2010
Language: English

Citation: V. I. Burenkov, A. Senouci, T. V. Tararykova, “Hardy-type inequality for $0<p<1$ and hypodecreasing functions”, Eurasian Math. J., 1:3 (2010), 27–42

Citation in format AMSBIB
\Bibitem{BurSenTar10}
\by V.~I.~Burenkov, A.~Senouci, T.~V.~Tararykova
\paper Hardy-type inequality for $0<p<1$ and hypodecreasing functions
\jour Eurasian Math. J.
\yr 2010
\vol 1
\issue 3
\pages 27--42
\mathnet{http://mi.mathnet.ru/emj27}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2904765}
\zmath{https://zbmath.org/?q=an:1273.47057}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. Azzouz, B. Halim, A. Senouci, “An inequality for the weighted Hardy operator for $0<p<1$”, Eurasian Math. J., 4:3 (2013), 127–131  mathnet
    2. R. A. Bandaliev, “On Hardy-type inequalities in weighted variable exponent spaces $L_{p(x),\omega}$ for $0<p(x)<1$”, Eurasian Math. J., 4:4 (2013), 5–16  mathnet
    3. Azzouz N., Burenkov V.I., Senouci A., “a Weighted Hardy-Type Inequality For 0 < P < 1 With Sharp Constant”, Math. Inequal. Appl., 18:2 (2015), 787–799  crossref  mathscinet  zmath  isi  elib
  • Eurasian Mathematical Journal
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