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Mathematical Notes

, Volume 60, Issue 4, pp 363–371 | Cite as

Interpolation of bilinear operators in Marcinkiewicz spaces

  • S. V. Astashkin
  • Yu. E. Kim
Article
  • 42 Downloads

Abstract

A theorem on interpolation of bilinear operators in symmetric Marcinkiewicz spaces is proved. It follows from the general bilinear results for the Peetre and Peetre-Gustavsson interpolation functors.

Key words

Marcinkiewicz spaces Peetre interpolation functor bilinear operators 

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References

  1. 1.
    S. V. Astashkin, “Real interpolation of bilinear operators,”Mat. Zametki [Math. Notes],52, No. 1, 15–24 (1992).MATHMathSciNetGoogle Scholar
  2. 2.
    S. G. Krein, Yu. I. Petunin, and E. M. Semenov,Interpolation of Linear Operators [in Russian], Nauka, Moscow (1978).Google Scholar
  3. 3.
    F. Peetre, “Sur l'utilisation des suites inconditionellement sommables dans la théorie des espaces d'interpolation,”Rend. Sem. Mat. Univ. Padova.,46, 173–190 (1971).MathSciNetGoogle Scholar
  4. 4.
    F. Gustavsson and F. Peetre, “Interpolation of Orlicz Spaces,”Studia Math.,60, 33–59 (1977).MathSciNetGoogle Scholar
  5. 5.
    J. Bergh and J. Löfström,Interpolation Spaces. An Introduction, Springer-Verlag, Berlin-Heidelberg-New York (1976).Google Scholar
  6. 6.
    F. Peetre, “A theory of interpolation of normed spaces,”Notes Math.,39, 1–86 (1969).Google Scholar
  7. 7.
    S. Fanson, “Minimal and maximal methods of interpolation,”J. Funct. Anal.,44, 50–73 (1981).MathSciNetGoogle Scholar
  8. 8.
    Yu. A. Brudnyi and N. Ya. Kruglyak,Real Interpolation Functors, Deposited in VINITI, No. 2620-81, Moscow (1981).Google Scholar
  9. 9.
    V. I. Ovchinnikov, “The method of orbits in interpolation theory,”Math. Rept.,1, 349–515 (1984).MATHMathSciNetGoogle Scholar
  10. 10.
    V. I. Dmitriev and V. I. Ovchinnikov, “Interpolation in the spaces of the real method,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],246, No. 4, 794–797 (1979).MathSciNetGoogle Scholar
  11. 11.
    M. Milman, “Tensor products of function spaces,”Bull. Amer. Math. Soc.,82, No. 4, 626–628 (1976).MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • S. V. Astashkin
    • 1
  • Yu. E. Kim
    • 1
  1. 1.Samara State UniversityUSSR

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