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Mat. Sb. (N.S.), 1988, Volume 136(178), Number 2(6), Pages 227–240 (Mi msb1738)  

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

Interpolation theorems for the spaces $L_{p,q}$

V. I. Ovchinnikov


Abstract: A sharp or optimal interpolation theorem is proved for the Lorentz spaces $L_{p,q}$, generalizing the Marcinkiewicz theorem and refining the Riesz–Thorin theorem and the Stein–Weiss theorem. This theorem extends to the spaces $\overline X_{\theta,p}$ of the real method constructed from any Banach pair; thus it extends also to Besov spaces.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Sbornik, 1989, 64:1, 229–242

Bibliographic databases:

UDC: 517.982.27
MSC: 46E35, 46E30
Received: 18.08.1986

Citation: V. I. Ovchinnikov, “Interpolation theorems for the spaces $L_{p,q}$”, Mat. Sb. (N.S.), 136(178):2(6) (1988), 227–240; Math. USSR-Sb., 64:1 (1989), 229–242

Citation in format AMSBIB
\Bibitem{Ovc88}
\by V.~I.~Ovchinnikov
\paper Interpolation theorems for the spaces $L_{p,q}$
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 2(6)
\pages 227--240
\mathnet{http://mi.mathnet.ru/msb1738}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=954926}
\zmath{https://zbmath.org/?q=an:0668.46042|0657.46056}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 1
\pages 229--242
\crossref{https://doi.org/10.1070/SM1989v064n01ABEH003304}


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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. Mastylo M., Milman M., “Interpolation of Real Method Spaces via Some Ideals of Operators”, Studia Math., 136:1 (1999), 17–35  mathscinet  zmath  isi
    2. Defant A., Mastylo M., Michels C., “Summing Inclusion Maps Between Symmetric Sequence Spaces”, Trans. Am. Math. Soc., 354:11 (2002), 4473–4492  crossref  mathscinet  zmath  isi
    3. Defant A., Mastylo M., Michels C., “Applications of Summing Inclusion Maps to Interpolation of Operators”, Q. J. Math., 54:Part 1 (2003), 61–72  crossref  mathscinet  isi
    4. Kussainova L., Ospanova A., “Interpolation Theorems For Weighted Sobolev Spaces”, World Congress on Engineering, Wce 2015, Vol i, Lecture Notes in Engineering and Computer Science, eds. Ao S., Gelman L., Hukins D., Hunter A., Korsunsky A., Int Assoc Engineers-Iaeng, 2015, 25–28  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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