Mathematical Notes

, Volume 77, Issue 5–6, pp 809–816 | Cite as

Interpolation of Rational Approximation Spaces Belonging to the Besov Class

  • V. L. Krepkogorskii


The Peetre real interpolation method is realized for the Besov class of spaces of analytic functions on the circle. We obtain a description of interpolation norms with the help of difference-differential constructions. We consider rational approximation spaces in the BMOA and H p norms.

Key words

rational approximation space analytic function Besov space interpolation norm BMO space BMOA norm Hp norm 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. V. Peller, “Hankel operators of class σp and their applications (rational approximation, Gaussian processes, problem of majorization of operators),” Mat. Sb. [tMath. USSR-Sb.], 113 (1980), no. 4, 538–581.Google Scholar
  2. 2.
    V. V. Peller, “The description of Hankel operators of class σp for p > 0, the study of the rate of rational approximation and other applications,” Mat. Sb. [Math. USSR-Sb.], 122 (1983), no. 4, 481–510.Google Scholar
  3. 3.
    A. A. Pekarskii, “The classes of analytic functions-defined by best approximations in H pMat. Sb. [Math. USSR-Sb.], 127 (1985), no. 1, 3–39.Google Scholar
  4. 4.
    A. A. Pekarskii, “Chebyshev rational approximations in the disk, on the circle, and on the closed interval,” Mat. Sb. [Math. USSR-Sb.], 133 (1987), no. 1, 86–102.Google Scholar
  5. 5.
    Yu. V. Netrusov, “Interpolation (real-variable method) of spaces of smooth functions,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 325 (1992), no. 6, 1120–1123.Google Scholar
  6. 6.
    Yu. V. Netrusov, “Nonlinear approximation of functions from the Besov-Lorentz spaces in the uniform metric,” Zap. Nauchn. Sem. LOMI, 204 (1993), 61–81.Google Scholar
  7. 7.
    H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Birkhauser, Berlin, 1977.Google Scholar
  8. 8.
    J. Bergh and J. Lofstrom, Interpolation Spaces. An Introduction, Springer-Verlag, Berlin-Heidelberg-New York, 1976.Google Scholar
  9. 9.
    V. L. Krepkogorskii, “Interpolation in Lizorkin-Triebel and Besov spaces,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 185 (1994), no. 7, 63–76.Google Scholar
  10. 10.
    P. Oswald, “On Besov-Hardy-Sobolev spaces of analytic functions in the unit disc,” Czechoslovak. Math. J., 33 (108) (1983), no. 3, 408–426.Google Scholar
  11. 11.
    D. Freitag, “Real interpolation of weighted L p-spaces,” Math. Nachr., 86 (1978), 15–18.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • V. L. Krepkogorskii
    • 1
  1. 1.Kazan BranchMilitary Artillery UniversityKazanRussia

Personalised recommendations