Chebyshev inequalities in symmetric spaces

  • Yu. G. Kuritsyn
  • Yu. I. Petunin
  • E. M. Semenov


The characterization (by means of inequalities) of some special Banach spaces is investigated.


Banach Space Symmetric Space Chebyshev Inequality Special Banach Space 
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Literature cited

  1. 1.
    S. G. Krein, Yu. I. Petunin, and E. M. Semenov, “Hyperscales for Banach Lattices,” Dokl. Akad. Nauk SSSR,170, No. 12, 265–267 (1966).Google Scholar
  2. 2.
    E. M. Semenov, “A scale for spaces with interpolation properties,” Dokl, Akad Nauk SSSR,148, No. 15, 1038–1041 (1963).Google Scholar
  3. 3.
    G. G. Lorentz, “Some new functional spaces,” Ann. of Math. (2),51, 36–55 (1950).Google Scholar
  4. 4.
    G. G. Lorentz, “On the theory of spaces Λ,” Pacific J. of Math.,1, 411–429 (1951).Google Scholar
  5. 5.
    W. Luxemburg and A. Zaanen, “Compactness of integral operators in Banach functional spaces,” Math. Ann.,149 (2), 150–180 (1963).Google Scholar
  6. 6.
    E. M. Semenov, “Imbedding theorems for Banach spaces of measurable functions,” Dokl. Akad. Nauk SSSR,156, No. 6, 1292–1295 (1964).Google Scholar
  7. 7.
    Yu. I. Petunin, “The contiguity of three Banach spaces,” Dokl. Akad Nauk SSSR,170, No. 3, 516–519 (1966).Google Scholar
  8. 8.
    S. G. Krein and Yu. I. Petunin, “A criterion for the contiguity of two Banach spaces,” Dokl. Akad. Nauk SSSR,139, 1295–1298 (1961).Google Scholar
  9. 9.
    S. G. Krein and Yu. I. Petunin, “The concept of a minimal scale for Banach spaces,” Dokl. Akad. Nauk SSSR,154, No. 1, 30–33 (1964).Google Scholar
  10. 10.
    M. D. Kendall and A. Stewart, Theory of Distributions [Russian translation], Nauka, Moscow (1966).Google Scholar
  11. 11.
    A. B. Kogan, Yu. I. Petunin, and O. G. Chorayan, “Investigation of impulse activity of neurons by the use of random-process theory,” Biofizika,11, No. 5, 887–893 (1966).Google Scholar
  12. 12.
    B. S. Mityagin, “An interpolation theorem for modular spaces,” Matem. Sb.,66, No. 4, 473–482 (1965).Google Scholar

Copyright information

© Consultants Bureau 1972

Authors and Affiliations

  • Yu. G. Kuritsyn
    • 1
  • Yu. I. Petunin
    • 1
  • E. M. Semenov
    • 1
  1. 1.Voronezh State UniversityUSSR

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