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The theory of interpolation spaces — its origin, prospects for the future

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Interpolation Spaces and Allied Topics in Analysis

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References

  1. Aronszajn, N., Gagliardo, E.: Interpolation spaces and interpolation methods. Ann. Mat. Pura Appl. 68, 51–118 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  2. Bergh, J., Löfström: Interpolation spaces. An introduction. (Grundlehren 223.) Berlin, Heidelberg, New York: Springer 1976.

    Chapter  Google Scholar 

  3. Brudnyĭ, Yu. A., Krugljak, N. Ya: Real interpolation functors. Dokl. Akad. Nauk SSSR 256, 14–17 (1981) [Russian].

    MathSciNet  Google Scholar 

  4. Brudnyĭ, Yu. A., Krugljak, N. Ya.: Real interpolation functors. Book manuscript [Russian; English translation in preparation].

    Google Scholar 

  5. Butzer, P. L., Berens, H.: Semi-groups of operators and approximation. (Grundlehren 145.) Berlin, Heidelberg, New York: Springer 1967.

    Book  MATH  Google Scholar 

  6. Ceausu, T., Gaspar, D.: A bibliographie of "interpolation of operators and applications in comutative a non-comutative harmonic analysis". Seminarul de Operatori Liniari si Analiza Armonica. Universitates din Timosoara. Facultatea de Stiinte ale Naturii. Sectia de Matematica. Timisoara: 1980.

    Google Scholar 

  7. Coifman, R., Cwikel, M., Rochberg, R., Sagher, Y., Weiss, G.: A theory of complex interpolation for families of Banach spaces. Advances Math. 43, 203–229 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  8. Janson, S.: Minimal and maximal methods of interpolation. J. Func. Anal. 14, 50–72 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  9. Jawerth, B.: in preparation.

    Google Scholar 

  10. Kreĭ, S. G., Petunin, Yu. I., Semenov, E.: Interpolation of linear operators. Moscow: Izdat. Nauka 1978 [Russian]; English translation: Providence: American mathematical Society 1982.

    Google Scholar 

  11. Lions, J.-L., Magenes, E.: Problemes aux limites non homogenes et applications, I. Paris: Dunod 1968.

    MATH  Google Scholar 

  12. Ovčinnikov, V. I.: The method of orbits in interpolation theory. Math. Reports 1, 349–515 (1984).

    MathSciNet  Google Scholar 

  13. Peetre, J.: Recent progress in real interpolation. In: Methods of Functional Analysis and Theory of Elliptic Equations. Proceedings of the International Meeting dedicated to the memory of professor Carlo Miranda. Naples, September 13–16, 1982. Edited by Donato Greco. Naples: Liguori 1983.

    Google Scholar 

  14. Triebel, H.: Interpolation theory. Function spaces. Differential operators. Berlin: VEB 1978.

    MATH  Google Scholar 

  15. Zygmund, A.: Trigonometric series, I–II. Cambridge: Cambridge University Press 1958.

    MATH  Google Scholar 

  16. Zygmund, A.: On a theorem of Marcinkiewicz concerning interpolation of operations. J. Math. Pures Appl. 35, 223–248 (1956).

    MathSciNet  MATH  Google Scholar 

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Michael Cwikel Jaak Peetre

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© 1984 Springer-Verlag

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Peetre, J. (1984). The theory of interpolation spaces — its origin, prospects for the future. In: Cwikel, M., Peetre, J. (eds) Interpolation Spaces and Allied Topics in Analysis. Lecture Notes in Mathematics, vol 1070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099088

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  • DOI: https://doi.org/10.1007/BFb0099088

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13363-6

  • Online ISBN: 978-3-540-38913-2

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