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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 449–464 (Mi semr1070)  

Real, complex and functional analysis

Brezis–Marcus type inequalities with Lamb constant

R. G. Nasibullin

Kazan Federal University, 18, Kremlyovskaya str., Kazan, 420008, Russia

Abstract: Hardy-type inequalities with an additional term are proved for compactly supported smooth functions on open convex sets in the Euclidean space. We obtain one-dimensional $L_p$-inequalities and their multidimensional analogs on arbitrary domains, on regular sets, on domains with $\theta$-cone condition and on convex domains. We use Bessel's function and the Lamb constant.

Keywords: Hardy inequality, additional term, Bessel function, Lamb constant, distance function, inner radius.

Funding Agency Grant Number
Russian Science Foundation 18-11-00115
This work is supported by the Russian Science Foundation under grant 18-11-00115.


DOI: https://doi.org/10.33048/semi.2019.16.027

Full text: PDF file (191 kB)
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Bibliographic databases:

UDC: 517.5
MSC: 26D15
Received December 30, 2018, published April 2, 2019
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Citation: R. G. Nasibullin, “Brezis–Marcus type inequalities with Lamb constant”, Sib. Èlektron. Mat. Izv., 16 (2019), 449–464

Citation in format AMSBIB
\Bibitem{Nas19}
\by R.~G.~Nasibullin
\paper Brezis--Marcus type inequalities with Lamb constant
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 449--464
\mathnet{http://mi.mathnet.ru/semr1070}
\crossref{https://doi.org/10.33048/semi.2019.16.027}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000463139000001}


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