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Mat. Tr., 2001, Volume 4, Number 1, Pages 122–173 (Mi mt8)  

This article is cited in 4 scientific papers (total in 4 papers)

Interpolation of Weighted Sobolev Spaces

S. G. Pyatkov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: In the present article, we describe the spaces $(H_{p,\Psi}^m(\Omega),L_{p,\omega}(\Omega))_{\theta,p}$, where the norms on $H_{p,\Psi}^m(\Omega)$ and on $L_{p,\omega}(\Omega)$ are defined as follows:
\begin{align*} \|u\|_{H_{p,\Psi}^m(\Omega)}^p&=\int_{\Omega}\sum_{|\alpha|\le m}\omega_{\alpha}|D^{\alpha}u(x)|^p dx,
\|u\|_{L_{p,\omega}(\Omega)}^p&=\int_{\Omega}\omega(x)|u(x)|^p dx, \end{align*}
with $\omega_{\alpha}$, $\omega$ continuous positive functions on $\Omega$. The results obtained are applicable to studying elliptic eigenvalue problems with an indefinite weight function.

Key words: interpolation space, weighted Sobolev space, Besov space, Hardy inequality.

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English version:
Siberian Advances in Mathematics, 2000, 10:3, 83–132

Bibliographic databases:

UDC: 517.95
Received: 08.12.1998

Citation: S. G. Pyatkov, “Interpolation of Weighted Sobolev Spaces”, Mat. Tr., 4:1 (2001), 122–173; Siberian Adv. Math., 10:3 (2000), 83–132

Citation in format AMSBIB
\Bibitem{Pya01}
\by S.~G.~Pyatkov
\paper Interpolation of Weighted Sobolev Spaces
\jour Mat. Tr.
\yr 2001
\vol 4
\issue 1
\pages 122--173
\mathnet{http://mi.mathnet.ru/mt8}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1850151}
\zmath{https://zbmath.org/?q=an:1066.46017|0976.46008}
\elib{http://elibrary.ru/item.asp?id=9532565}
\transl
\jour Siberian Adv. Math.
\yr 2000
\vol 10
\issue 3
\pages 83--132


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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. S. G. Pyatkov, “Elliptic Eigenvalue Problems Involving an Indefinite Weight Function”, Siberian Adv. Math., 10:4 (2000), 134–150  mathnet  mathscinet  zmath  elib
    2. A. I. Parfenov, “On an embedding criterion for interpolation spaces and application to indefinite spectral problems”, Siberian Math. J., 44:4 (2003), 638–644  mathnet  crossref  mathscinet  zmath  isi
    3. A. V. Chueshev, “Koertsitivnye svoistva obyknovennogo differentsialnogo operatora chetnogo poryadka”, Vestn. NGU. Ser. matem., mekh., inform., 5:2 (2005), 86–105  mathnet
    4. Pyatkov S.C., “Interpolation of Sobolev Spaces and Indefinite Elliptic Spectral Problems”, Recent Advances in Operator Theory in Hilbert and Krein Spaces, Operator Theory Advances and Applications, 198, 2010, 265–290  mathscinet  zmath  isi
  • Математические труды Siberian Advances in Mathematics
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