Skip to main content
SpringerLink
Log in

On the interpolation of some generalized function spaces of different anisotropy

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

In the paper, the interpolation properties of the spacesH s p (v; ℝ n ) of Sobolev-Liouville type and the spacesB s p, q (μ ℝ n ) of Nikol'skii-Besov type generated by functions of polynomial growth that are infinitely differentiable outside of the origin are studied. Interpolation formulas for the pairs {H(v o ),H(v 1)} and {B(μ0),B(μ1)} of spaces of the above types for which the anisotropies of the interpolated spaces do not depend on each other are proved. The investigated spaces, for certain specification of the generating functions, coincide with the classical (isotropic and anisotropic) Sobolev-Liouville and Nikol'skii-Besov spaces.

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

References

  1. S. M. Nikol'skii,Approximation of Functions of Many Variables and Embedding Theorems [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  2. H. Triebel,Theory of Function Spaces Birkhäuser Verlag, Basel-Boston-Stuttgart (1983).

    Google Scholar 

  3. A. G. Bagdasaryan, “Interpolation of some function spaces with different anisotropies,”Izv. Akad. Armyan. SSR Ser. Mat.,27, No. 4, 49–58 (1992).

    MATH  MathSciNet  Google Scholar 

  4. H. Triebel, “General function spaces III (spacesB p, q s(x),F p, q s(x),1<p<∞: basic properties),”Anal. Math.,3, 221–249 (1977).

    MATH  MathSciNet  Google Scholar 

  5. A. G. Bagdasaryan, “Interpolation and traces of functions from some anisotropic function spaces,”Izv. Akad. Armyan. SSR Ser. Mat., [Soviet J. Contemporary Math. Anal.],23, No. 4, 353–365 (1988).

    MATH  MathSciNet  Google Scholar 

  6. A. G. Bagdasaryan, “Embedding theorems for certain generalized function spaces,”Izv. Nats. Akad. Nauk Armenii Mat.,29, No. 3, 1–10 (1994).

    MATH  MathSciNet  Google Scholar 

  7. J. Bergh and J. Löfström,Interpolation Spaces. An Introduction, Springer-Verlag, Berlin, (1976).

    Google Scholar 

  8. P. I. Lizorkin, “(L p ,L q )-multipliers of Fourier integrals,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],152, No. 4, 808–811 (1963).

    MATH  MathSciNet  Google Scholar 

  9. H. Triebel,Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam-New York (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Erevan State University, Russia

    A. G. Bagdasaryan

Authors
  1. A. G. Bagdasaryan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 666–672, November, 1997.

Translated by A. I. Shtern

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bagdasaryan, A.G. On the interpolation of some generalized function spaces of different anisotropy. Math Notes 62, 557–561 (1997). https://doi.org/10.1007/BF02361292

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02361292

Key words

Search

Navigation