Skip to main content
SpringerLink
Log in
Book cover

Complex Analysis Joensuu 1987 pp 52–68Cite as

Remarks on Sobolev imbedding inequalities

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1351))

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. R. Adams, A trace inequality for generalized potentials. Studia Math. 48 (1973), 99–105.

    MathSciNet  MATH  Google Scholar 

  2. O. V. Besov, V. P. Ilin, S. M. Nikolskii, Integral representation of functions and imbedding theorems. (Russian) Izdat. Nauka, Moscow, 1975.

    Google Scholar 

  3. B. Bojarski, Pointwise differentiability of weak solutions of elliptic divergence type equations. Bull. Polish Acad. Sci. Math. 33:1–2 (1985), 1–6.

    MathSciNet  MATH  Google Scholar 

  4. B. Bojarski, Sharp maximal operator of fractional order and Sobolev imbedding inequalities. ibid. 33:1–2 (1985), 7–16.

    MathSciNet  MATH  Google Scholar 

  5. B. Bojarski, Remarks on Markov's inequalities and some properties of polynomials. ibid. 33:7–8 (1985), 355–365.

    MathSciNet  MATH  Google Scholar 

  6. B. Bojarski, Remarks on local function spaces. Proceedings of the Function Space Conference (Lund, 1986), Lecture Notes in Math., Springer-Verlag (to appear).

    Google Scholar 

  7. B. Bojarski, T. Iwaniec, Analytic foundations of the theory of quasiconformal mappings in Rn. Ann. Acad. Sci. Fenn. Ser. A I Math. 8 (1983), 257–324.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Boman, Lp-estimates for very strongly elliptic systems. J. Analyse Math. (to appear).

    Google Scholar 

  9. Ju. A. Brudnyj, I. M. Gansburg, On an extremal problem for polynomials of n variables. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 344–355.

    MathSciNet  Google Scholar 

  10. V. I. Burenkov, Sobolev's integral representation and Taylor's formula. (Russian) V. Trudy Mat. Inst. Steklov. 131 (1974), 33–38.

    MathSciNet  MATH  Google Scholar 

  11. R. Coifman, C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals. Studia Math. 51 (1974), 241–250.

    MathSciNet  MATH  Google Scholar 

  12. F. Gehring, O. Martio, Lipschitz classes and quasiconformal mappings. Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 203–219.

    Article  MathSciNet  MATH  Google Scholar 

  13. G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities. Cambridge, 1934.

    Google Scholar 

  14. T. Iwaniec, C. A. Nolder, Hardy-Littlewood inequality for quasiregular mappings in certain domains in Rn. Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 267–282.

    Article  MathSciNet  MATH  Google Scholar 

  15. F. John, On quasi-isometric mappings I, II. Comm. Pure Appl. Math. 21 (1968), 77–100, ibid. 22 (1969), 265–278.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Lehtonen, Embedding of Sobolev spaces into Lipschitz spaces. Preprint (University of Jyväskylä, 1986).

    Google Scholar 

  17. B. Mandelbrot, The fractal geometry of nature. Freeman, San Fransisco, 1982.

    MATH  Google Scholar 

  18. O. Martio, Definitions for uniform domains. Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), 179–205.

    Article  MathSciNet  MATH  Google Scholar 

  19. O. Martio, John domains, bilipschitz balls and Poincaré inequality. Rev. Roum. Math. Pures Appl. (to appear).

    Google Scholar 

  20. V. G. Mazja, Einbettungssätze für Sobolewsche Räume. Teil 1. Teubner, Leipzig, 1979.

    MATH  Google Scholar 

  21. V. G. Mazja, Prostranstva S. L. Soboleva. Izdat. Leningr. Univ., Leningrad, 1985. English translation: Sobolev Spaces. Springer-Verlag, 1986.

    Google Scholar 

  22. B. Muckenhoupt, Weighted norm inequalities for Hardy maximal function. Trans. Amer. Math. Soc. 165 (1972), 207–226.

    Article  MathSciNet  MATH  Google Scholar 

  23. B. Muckenhoupt, R. L. Wheeden, Weighted norm inequalities for fractional integrals. Trans. Amer. Math. Soc. 192 (1974), 261–274.

    Article  MathSciNet  MATH  Google Scholar 

  24. O. Nikodym, Sur une classe de fonctions considerée dans le problème de Dirichlet. Fund. Math. 21 (1933), 129–150.

    MATH  Google Scholar 

  25. H. Reimann, Functions of bounded mean oscillation and quasiconformal mappings. Comment. Math. Helv. 49 (1974), 260–276.

    Article  MathSciNet  MATH  Google Scholar 

  26. Ju. G. Rešetniak, Stability theorems in geometry and analysis. (Russian) Nauka Sibirsk. Otdel., Novosibirsk, 1982.

    Google Scholar 

  27. Ju. G. Rešetniak, Integral representations of differentiable functions in domains with non-smooth boundary. (Russian) Sibirsk. Mat. Zh. 21:6 (1980), 108–116.

    MathSciNet  Google Scholar 

  28. Ju. G. Rešetniak, Remarks on integral representations of differentiable functions in several variables. (Russian) Sibirsk. Mat. Zh. 25:5 (1984), 198–200.

    MathSciNet  Google Scholar 

  29. Ju. G. Rešetniak, Mappings with bounded distortion. Science, Moscow, 1981.

    Google Scholar 

  30. S. L. Sobolev, Some applications of functional analysis in mathematical physics. (Russian) Izdat. Leningrad. Gos. Univ., Leningrad, 1950.

    Google Scholar 

  31. E. Stein, Singular integrals and differentiability properties of functions. Princeton University Press, 1970.

    Google Scholar 

  32. J. O. Strömberg, A. Torchinsky, Weights, sharp maximal functions and Hardy spaces. Bull. Amer. Math. Soc. 3 (1980), 1053–1056.

    Article  MathSciNet  MATH  Google Scholar 

  33. J. Väisälä, Lectures on n-dimensional quasiconformal mappings. Lecture Notes in Math., 229, Springer-Verlag, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Warsaw, PKIN, IX p., 00901, Warszawa, Poland

    B. Bojarski

Authors
  1. B. Bojarski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ilpo Laine Tuomas Sorvali Seppo Rickman

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Bojarski, B. (1988). Remarks on Sobolev imbedding inequalities. In: Laine, I., Sorvali, T., Rickman, S. (eds) Complex Analysis Joensuu 1987. Lecture Notes in Mathematics, vol 1351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081242

Download citation

  • DOI: https://doi.org/10.1007/BFb0081242

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50370-5

  • Online ISBN: 978-3-540-45992-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation