Skip to main content
Log in

Convexity and concavity of Banach ideal spaces and imbedding theorems

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. B. Maurey, “Type et cotype dans les espaces munis de structures locales inconditionelles,” Séminaire Maurey-Schwartz 1973–1974: Espaces L p, applications radonifiantes et géométrie des espaces de Banach, Exp. Nos. 24 et 25, 25 pp. Centre de Math., École Polytech., Paris, 1974.

    Google Scholar 

  2. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. II. Function Spaces, Springer, Berlin (1979).

    Google Scholar 

  3. A. V. Bukhvalov, A. I. Veksler, and G. Ya. Lozanovskii, “Banach lattices — some Banach aspects of the theory,” Usp. Mat. Nauk,34, No. 2, 137–183 (1979).

    Google Scholar 

  4. S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  5. O. V. Besov, V. P. Il'in, and S. M. Nikol'skii, Integral Representations of Functions and Imbedding Theorems, Vols. I and II, Wiley, New York (1978 and 1979).

    Google Scholar 

  6. S. G. Krein, J. I. Petunin, and E. M. Semenov, Interpolation of Linear Operators, Operators. Am. Math. Soc., Providence (1982).

    Google Scholar 

  7. L. V. Kantorovich, and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  8. M. Z. Berkolaiko, “Inequalities for entire functions of exponential type in symmetric spaces,” Trudy Mat. Inst. Akad. Nauk SSSR,161, 3–17 (1983).

    Google Scholar 

  9. P. I. Lizorkin, “Multipliers of Fourier integrals and estimates of convolutions in spaces with mixed norm. Applications,” Izv. Akad. Nauk SSSR, Ser. Mat.,34, 218–247 (1970).

    Google Scholar 

  10. A. V. Bukhvalov, “Interpolation of operators in spaces of vector functions, with applications to singular integral operators,” Dokl. Akad. Nauk SSSR,278, No. 3, 523–526 (1984).

    Google Scholar 

  11. H. Triebel, Theory of Function Spaces, Birkhäuser, Basel (1983).

    Google Scholar 

  12. M. Z. Berkolaiko, “Imbedding theorems for various metrics of measurements and generalized Besov spaces,” Trudy Mat. Inst. Akad. Nauk SSSR,161, 18–28 (1983).

    Google Scholar 

  13. S. Ya. Novikov, “Cotype and type of Lorentz function spaces,” Mat. Zametki,32, No. 2, 213–221 (1982).

    Google Scholar 

  14. J. Bergh and J. Lofstrom, Interpolation Spaces. An Introduction, Springer, Berlin (1976).

    Google Scholar 

Download references

Authors

Additional information

Voronezh. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 3, pp. 11–18, May–June, 1990.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berkolaiko, M.Z. Convexity and concavity of Banach ideal spaces and imbedding theorems. Sib Math J 31, 373–379 (1990). https://doi.org/10.1007/BF00970343

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00970343

Keywords

Navigation