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Eurasian Math. J., 2019, Volume 10, Number 1, Pages 52–58 (Mi emj322)  

This article is cited in 1 scientific paper (total in 1 paper)

Hardy type inequality with sharp constant for $0 < p < 1$

A. Senouciab, N. Azzouzacb

a Department of Mathematics, Ibn Khaldoun University, Tiaret, Algeria
b Laboratoire LIM
c Department of Technologies, University of Sidi Bel Abbes - Algeria

Abstract: 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.

Keywords and phrases: Hardy operator, Hardy-type inequality, sharp constant.

DOI: https://doi.org/10.32523/2077-9879-2019-10-1-52-58

Full text: PDF file (408 kB)
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Bibliographic databases:

MSC: 35J20, 35J25
Received: 25.11.2017
Revised: 15.04.2019
Language:

Citation: A. Senouci, N. Azzouz, “Hardy type inequality with sharp constant for $0 < p < 1$”, Eurasian Math. J., 10:1 (2019), 52–58

Citation in format AMSBIB
\Bibitem{SenAzz19}
\by A.~Senouci, N.~Azzouz
\paper Hardy type inequality with sharp constant for $0 < p < 1$
\jour Eurasian Math. J.
\yr 2019
\vol 10
\issue 1
\pages 52--58
\mathnet{http://mi.mathnet.ru/emj322}
\crossref{https://doi.org/10.32523/2077-9879-2019-10-1-52-58}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000468977300004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85066285703}


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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. R. G. Nasibullin, “Sharp conformally invariant Hardy-type inequalities with remainders”, Eurasian Math. J., 12:3 (2021), 46–56  mathnet  crossref
  • Eurasian Mathematical Journal
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