Functional Analysis and Its Applications

, Volume 47, Issue 2, pp 157–159 | Cite as

Spaces of smooth functions generated by nonhomogeneous differential expressions

  • S. V. Kislyakov
  • D. V. Maksimov
  • D. M. Stolyarov
Article

Abstract

A Sobolev-type embedding theorem is established, which differs from classical statements in that the assumptions are imposed on linear combinations of the form \(\sum {a_j D^{a_j f_j } } \) with different functions fj and different multi-indices αj. It is applied to a classification problem for spaces of smooth functions generated by finite collections of differential expressions.

Key words

space of smooth functions isomorphism Sobolev embedding. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer-Verlag, Berlin, 1979.MATHCrossRefGoogle Scholar
  2. [2]
    S. V. Kislyakov, Funkts. Anal. Prilozhen., 9:4 (1975), 22–27; English transl.: Functional Anal. Appl., 9:4 (1975), 290–294.Google Scholar
  3. [3]
    S. V. Kislyakov and D. V. Maksimov, Zap. Nauchn. Sem. POMI, 327 (2005), 78–97; English transl.: J. Math. Sci. (N.Y.), 139:2 (2006), 6406–6416.MATHGoogle Scholar
  4. [4]
    S. V. Kislyakov and D. V. Maksimov, POMI preprint 6/2009.Google Scholar
  5. [5]
    D. V. Maksimov, Zap. Nauchn. Sem. POMI, 333 (2006), 62–65; English transl.: J. Math. Sci. (N.Y.), 141:5 (2007), 1543–1544.MATHGoogle Scholar
  6. [6]
    S. V. Kislyakov and N. G. Sidorenko, Sibirsk. Mat. Zh., 29:3 (1988), 64–77; English transl.: Siberian Math. J., 29:3 (1988), 384–394.MathSciNetMATHGoogle Scholar
  7. [7]
    A. Pełczyński and K. Senator, Studia Math., 84:2 (1986), 169–215.MathSciNetMATHGoogle Scholar
  8. [8]
    V. A. Solonnikov, Zap. Nauchn. Sem. LOMI, 27 (1972), 194–210.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • S. V. Kislyakov
    • 1
  • D. V. Maksimov
    • 2
  • D. M. Stolyarov
    • 3
  1. 1.St. Petersburg Department of the V. A. Steklov Mathematical InstituteSt. PetersburgRussia
  2. 2.St. Petersburg State Polytechnical UniversitySt. PetersburgRussia
  3. 3.P. L. Chebyshev research laboratory SPbGUSt. PetersburgRussia

Personalised recommendations