Skip to main content
SpringerLink
Log in

Free interpolation in some spaces of smooth functions

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

This paper is devoted to a study of the traces of functions from the classes B lp,π or F lp,π on a set A ⊂ ℝn. In the proofs the results of Netrusov[Zap. Nauchn. Semin. LOMI 204, 61–81 (1992)] are essentially used. We consider the following questions:

  1. (1)

    Under what conditions on a compact set K, K ⊂ ℝn, do the traces on K of functions from B lp θ∩ℂ(ℝn) (or F lp θ∩ℂ(ℝn) fill in the entire space C(K)?

  2. (2)

    Under what conditions on a Borel set A does the space of traces on A of functions from F lp,π , 0<p≤1, coincide with some quasi-Banach lattice?

  3. (3)

    What is the description of the space of traces in the latter case? See Theorem 2.1 for an answer to (1) and Theorem 2.2 for an answer to (2) and (3). In the last part of the paper we prove counterparts of Theorems 2.1 and 2.2 for spaces of analytic functions Bibliography: 14 titles.,

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature Cited

  1. Yu. V. Netrusov, “Nonlinear approximation of functions from Besov-Lorentz spaces in the uniform metric,”Zap. Nauchn. Semin. LOMI,204, 61–81 (1992).

    Google Scholar 

  2. Yu. V. Netrusov, “Sets of singularities of functions from spaces of the Besov and Lisorkin-Triebel type”,Tr. Mat. Inst. Akad. Nauk SSSR,187, 162–178 (1989).

    MathSciNet  Google Scholar 

  3. M. Frasier and B. Gawerth, “A discrete transform and decompositions of distribution spaces,”J. Funct. Anal.,93, No. 1, 34–170 (1990).

    MathSciNet  Google Scholar 

  4. H. Triebel,Theory of Function Spaces, Akad. Verl. Geest & Portig K.-G., Leipzig (1983).

    Google Scholar 

  5. D. R. Adams, “The classification problem for the capacity associated with the Besov and Triebel-Lizorkin spaces,” in:Approximation and Function Spaces, PWN-Polish scientific publishers, Banach center publications,22 (1989), pp. 9–24.

  6. Yu. V. Netrusov, “Metric estimates of set capacities in the Besov-spaces,”Tr. Mat. Inst. Akad. Nauk SSSR,190, 159–185 (1989).

    MATH  MathSciNet  Google Scholar 

  7. Yu. V. Netrusov, “Estimates of capacities concerning the Besov spaces,”Zap. Nauchn. Semin. LOMI,201, 124–156 (1992).

    MATH  Google Scholar 

  8. D. R. Adams, “Exeptional sets for Besov spaces,”Lect. Notes Math.,1043, 515–518 (1984).

    Google Scholar 

  9. C. Fefferman and E. M. Stein, “H p spaces of several variables,”Acta Math.,129, No. 3, 137–194 (1972).

    MathSciNet  Google Scholar 

  10. J. R. Dorronsoro, “On the differentiability of Lipschitz-Besov functions,”Trans. Amer. Math. Soc.,303, No. 1, 229–240 (1987).

    MATH  MathSciNet  Google Scholar 

  11. V. V. Peller and S. V. Khrushchev, “Hankel operators, best approximations, and stationary Gaussian processes,”Usp. Math. Nauk,37, No. 1, 53–124 (1982).

    MathSciNet  Google Scholar 

  12. J. Garnett,Bounded Analytic Functions, Academic Press, New York (1981).

    Google Scholar 

  13. T. Sjödin, “Bessel potentials and extension of continuous functions on compact sets,”Ark. Mat.,13, No. 2, 263–271 (1975).

    MATH  MathSciNet  Google Scholar 

  14. T. Sjödin, “Non-linear potential theory in Lebesgue spaces with mixed norm and extension of continuous functions on compact sets,” Report No. 5, University of Umeå (1987).

Download references

Authors
  1. Yu. V. Netrusov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 206, 1993, pp. 107–118.

Translated by E. Abakumov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Netrusov, Y.V. Free interpolation in some spaces of smooth functions. J Math Sci 80, 1941–1950 (1996). https://doi.org/10.1007/BF02367009

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02367009

Keywords

Search

Navigation