Skip to main content
Log in

Imbedding theorems for abstract function spaces and the complete continuity of the imbedding operator

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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. S. L. Sobolev, “Some generalizations of imbedding theorems,” Fund. Math.,47, No. 3, 277–324 (1959).

    Google Scholar 

  2. V. B. Korotkov, “Direct and converse imbedding theorems for certain spaces of abstract set functions,” Dokl. Akad. Nauk SSSR,144, No. 4, 717–720 (1962).

    Google Scholar 

  3. V. B. Korotkov, “Abstract set functions and imbedding theorems,” Dokl. Akad. Nauk SSSR,146, No. 3, 531–534 (1962).

    Google Scholar 

  4. V. B. Korotkov, “Representation of continuous linear operators as abstract functions and imbedding theorems,” Dokl. Akad. Nauk SSSR,153, No. 2, 262–265 (1963).

    Google Scholar 

  5. V. B. Korotkov, “Tests for compactness in abstract function spaces and the complete continuity of the imbedding operator,” Dokl. Akad. Nauk SSSR,160, No. 3, 530–533 (1965).

    Google Scholar 

  6. J. Wloka, “Wektorwertige Sobolev-Slobodeckijsche Distributionen,” Math. Zeitschr.,98, No. 4, 303–319 (1967).

    Google Scholar 

  7. K. Vala, “On compact sets of compact operators,” Ann. Acad. Sci. Fennicae, Ser. A, I, Math.,351, 3–8 (1964).

    Google Scholar 

  8. S. L. Sobolev, Sur les Équations aux Dérivées Partielles Hyperboliques Nonlineaires, Roma (1961).

  9. J.-L. Lions, “Théoremes de trace et d'interpolation,” Annali Scuola Norm. Sup Pisa,12, 389–403 (1959).

    Google Scholar 

  10. A. A. Bokk, “An extension of an imbedding theorem of S. L. Sobolev,” Proceedings of the Third Siberian Conference on Mathematics and Mechanics [in Russian], Tomsk (1964), pp. 51–52.

  11. N. Bourbaki, Topological Vector Spaces [Russian translation], IL, Moscow (1959).

    Google Scholar 

  12. V. B. Korotkov, Direct and Converse Imbedding Theorems for Certain Abstract Function Spaces, Dissertation, Matem. Institute im. V. A. Steklov (1962).

  13. A. Clarkson, “Uniformly convex spaces,” Trans. Amer. Math. Soc.,40, No. 3, 396–414 (1936).

    Google Scholar 

  14. N. Dunford and J. Schwartz, Linear Operators: General Theory, Interscience (1960).

  15. S. Banach, Théorie des Operations Linéaires, Warsaw (1932).

  16. E. Hille and R. Phillips, Functional Analysis and Semigroups, American Math. Soc. (1957).

  17. V. I. Smirnov, A Course in Higher Analysis, Vol. 5, Fizmatgiz (1959).

  18. Ya. Kadlets and V. B. Korotkov, “Estimates of the s-numbers of imbedding operators and operators that increase smoothness,” Czech. Math. J.,18, 678–699 (1968).

    Google Scholar 

  19. L. D. Kudryavtsev, “The continuation of functions and the imbedding of classes of functions,” Dokl. Akad. Nauk SSSR,107, No. 4, 501–504 (1956).

    Google Scholar 

  20. L. D. Kudryavtsev, “Direct and converse imbedding theorems. Applications to the solution of elliptic equations by variational methods,” Trudy Mat. Inst. im V. A. Steklov,35, 1–181 (1959).

    Google Scholar 

  21. A. Grothendieck, “Produits tensoriels topologiques et espaces nucleaires,” Memoires Amer. Math. Soc.,16, 1–140 (1955).

    Google Scholar 

  22. I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Non-selfadjoint Operators, Nauka (1965).

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 10, No. 4, pp. 872–902, July–August, 1969.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Korotkov, V.B. Imbedding theorems for abstract function spaces and the complete continuity of the imbedding operator. Sib Math J 10, 640–663 (1969). https://doi.org/10.1007/BF00973871

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00973871

Keywords

Navigation