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Mat. Sb. (N.S.), 1985, Volume 128(170), Number 1(9), Pages 66–81 (Mi msb2018)  

This article is cited in 5 scientific papers (total in 5 papers)

Imbedding theorems for Banach spaces of infinitely differentiable functions

G. S. Balashova


Abstract: Algebraic conditions are obtained for imbedding of the spaces
$$ W^{\infty}\{a_n,p,r\}_{(G)}=\{u(x)\in C^\infty(G):\sum_{n=0}^\infty a_n\|D^nu\| _r^p<\infty\}, $$
where $G$ can be a closed interval, the line, a ray, or the circle. The imbedding conditions depend on the form of the domain.
Bibliography: 15 titles.

Full text: PDF file (664 kB)
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English version:
Mathematics of the USSR-Sbornik, 1987, 56:1, 63–78

Bibliographic databases:

UDC: 517.5
MSC: 46E35
Received: 19.04.1984

Citation: G. S. Balashova, “Imbedding theorems for Banach spaces of infinitely differentiable functions”, Mat. Sb. (N.S.), 128(170):1(9) (1985), 66–81; Math. USSR-Sb., 56:1 (1987), 63–78

Citation in format AMSBIB
\Bibitem{Bal85}
\by G.~S.~Balashova
\paper Imbedding theorems for Banach spaces of infinitely differentiable functions
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 128(170)
\issue 1(9)
\pages 66--81
\mathnet{http://mi.mathnet.ru/msb2018}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=805696}
\zmath{https://zbmath.org/?q=an:0615.46029}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 1
\pages 63--78
\crossref{https://doi.org/10.1070/SM1987v056n01ABEH003024}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. A. Dubinskii, “Sobolev spaces of infinite order”, Russian Math. Surveys, 46:6 (1991), 107–147  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Balashova G., “Limiting Behavior of Solutions of a Sequence of Differential-Equations of Infinite-Order”, Differ. Equ., 28:4 (1992), 518–528  mathnet  mathscinet  zmath  isi
    3. G. S. Balashova, “On conditions for extending the trace and imbedding for Banach spaces of infinitely differentiable functions”, Russian Acad. Sci. Sb. Math., 78:1 (1994), 91–112  mathnet  crossref  mathscinet  zmath  isi
    4. Bang H., “On Imbedding Theorems for Sobolev-Orlicz Spaces of Infinite Order”, Dokl. Akad. Nauk, 354:3 (1997), 316–319  mathnet  mathscinet  zmath  isi
    5. Balashova G., “On the Sobolev Spaces of Infinite Order”, Dokl. Akad. Nauk, 353:2 (1997), 151–152  mathnet  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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