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Quasiconformal mappings and extendability of functions in sobolev spaces

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References

  1. Ahlfors, L. V., Quasiconformal reflections,Acta Math., 109 (1963), 291–301.

    Article  MATH  MathSciNet  Google Scholar 

  2. Calderón, A. P., Lebesgue spaces of differentiable functions and distributions, inProc. Symp. Pure Math., Vol. IV, 1961, 33–49.

  3. — Estimates for singular integral operators in terms of maximal functions.Studia Math., 44 (1972), 563–582.

    MATH  MathSciNet  Google Scholar 

  4. Calderon, A. P. &Scott, R., Sobolev type inequalities forp>0.Studia Math., 62 (1978), 75–92.

    MathSciNet  MATH  Google Scholar 

  5. Gehring, F. W., Extensions of quasiconformal mappings in three space.J. Analyse Math., 14 (1965), 171–182.

    MATH  MathSciNet  Google Scholar 

  6. Gehring, F. W. Extension theorems for quasiconformal mappings inn-space.Proceedings of the International Congress of Mathematicians (Moscow, 1966), 313–318.

  7. — Extension theorems for quasiconformal mappings inn-space.J. Analyse Math., 19 (1967), 149–169.

    Article  MATH  MathSciNet  Google Scholar 

  8. Gehring, F. W. Characterizations of uniform domains. To appear.

  9. Gehring, F. W. &Väisälä, J., The coefficients of quasiconformality of domains in space.Acta Math., 114 (1965), 1–70.

    Article  MathSciNet  MATH  Google Scholar 

  10. — Hausdorff dimension and quasiconrormal mappings,J. London Math. Soc., 6 (1973), 504–512.

    MATH  MathSciNet  Google Scholar 

  11. Gol'dshtein, V. M., Latfullin, T. G. &Vodop'yanov, S. K., Criteria for extension of functions of the classL 12 from unbounded plain domains.Siberian Math. J. (English translation), 20: 2 (1979), 298–301.

    Article  MathSciNet  Google Scholar 

  12. Gol'dhtein, V. M., Reshetnyak, Yu. G. &Vodop'yanov, S. K., On geometric properties of functions with generalized first derivatives.Uspehi Mat. Nauk., 34: 1 (1979), 17–65. English translation inRussian Math. Surveys, 34: 1 (1979), 19–74.

    Google Scholar 

  13. Hestenes, M., Extension of the range of a differentiable function.Duke Math. J., 8 (1941), 183–192.

    Article  MATH  MathSciNet  Google Scholar 

  14. Jerison, D. & Kenig, C., Boundary behavior of harmonic functions in nontagentially accessible domains. Preprint.

  15. Jones, P. W., Extension theorems for BMO.Indiana Math. J., 29 (1980), 41–66.

    Article  MATH  Google Scholar 

  16. Lehto, O. &Virtanen, K. I.,Quasiconformal mappings in the plane. 2nd ed., Springer-Verlag, New York, 1973.

    MATH  Google Scholar 

  17. Lichtenstein, L., Eine elementare Bemerkung zur reelen Analysis.Math. Z., 30 (1919).

  18. Martio, O. & Sarvas, J., Injectivity theorems in the plane and space.Ann. Ann. Acad. Sci. Fenn. To appear.

  19. Mostow, G. D., Quasiconformal mappings inn-space and the rigidity of hyperbolic space forms.I.H.E.S. Publ. Math., 34 (1968), 53–104.

    MATH  MathSciNet  Google Scholar 

  20. Stein, E. M.,Singular integrals and differentiability properties of functions. Princeton University Press, Princeton. New Jersey, 1970.

    MATH  Google Scholar 

  21. Sullivan, D., The density at infinity of a discrete group of hyperbolic motions.I.H.E.S. Publ. Math., 50 (1979), 171–202.

    MATH  MathSciNet  Google Scholar 

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

  23. Whitney, H., Analytic extensions of differentiable functions defined in closed sets.Trans. Amer. Math. Soc., 36 (1934), 63–89.

    Article  MATH  MathSciNet  Google Scholar 

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  1. University of Chicago, Chicago, Illinois, USA

    Peter W. Jones

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  1. Peter W. Jones
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N.S.F. grant MCS-7905036.

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Jones, P.W. Quasiconformal mappings and extendability of functions in sobolev spaces. Acta Math. 147, 71–88 (1981). https://doi.org/10.1007/BF02392869

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