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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 4(8), Pages 642–652 (Mi msb2429)  

This article is cited in 6 scientific papers (total in 6 papers)

On estimates of interpolation orbits

V. I. Ovchinnikov


Abstract: In this paper the orbits for some pairs of spaces are described in the case when the latter cannot be described by the $K$-method. A new estimate from below is given for the orbits of arbitrary pairs of spaces, and it is shown to be sharp. New examples of classical pairs of spaces are found for which the interpolation orbits are not described by the $K$-method, and an interpolation theorem for scales of spaces is proved, which cannot be obtained by the complex method or the method of means, nor even by a combination of both.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 43:4, 573–583

Bibliographic databases:

UDC: 513.881
MSC: 46E35
Received: 20.02.1980

Citation: V. I. Ovchinnikov, “On estimates of interpolation orbits”, Mat. Sb. (N.S.), 115(157):4(8) (1981), 642–652; Math. USSR-Sb., 43:4 (1982), 573–583

Citation in format AMSBIB
\Bibitem{Ovc81}
\by V.~I.~Ovchinnikov
\paper On estimates of interpolation orbits
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 4(8)
\pages 642--652
\mathnet{http://mi.mathnet.ru/msb2429}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=629632}
\zmath{https://zbmath.org/?q=an:0493.46059}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 4
\pages 573--583
\crossref{https://doi.org/10.1070/SM1982v043n04ABEH002582}


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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. V. I. Ovchinnikov, “Interpolation theorems for the spaces $L_{p,q}$”, Math. USSR-Sb., 64:1 (1989), 229–242  mathnet  crossref  mathscinet  zmath
    2. L. Maligranda, V.I. Ovchinnikov, “On interpolation between L1 + L∞ and L1 ∩ L∞”, Journal of Functional Analysis, 107:2 (1992), 342  crossref
    3. Cwikel M., Nilsson P., “Interpolation of Weighted Banach Lattices”, Mem. Am. Math. Soc., 165:787 (2003), 1–105  mathscinet  isi
    4. M. A. Shubarin, “Usloviya interpolyatsionnosti dlya semeistv prostranstv Freshe”, Vladikavk. matem. zhurn., 9:2 (2007), 54–62  mathnet  mathscinet  elib
    5. V. I. Ovchinnikov, “Generalized Lions-Peetre interpolation construction and optimal embedding theorems for Sobolev spaces”, Sb. Math., 205:1 (2014), 83–100  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. V. I. Dmitriev, “On one transformation of parameter-spaces of real interpolation method”, Russian Math. (Iz. VUZ), 60:12 (2016), 36–42  mathnet  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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