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On univalent functions, Bloch functions and VMOA

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References

  1. Anderson, J.M., Clunie, J., Pommerenke, Ch.: On Bloch functions and normal functions. J. reine angew. Math.270, 12–37 (1974)

    MathSciNet  MATH  Google Scholar 

  2. Becker, J., Pommerenke, Ch.: Über die quasikonforme Fortsetzung schlichter Funktionen. (to appear)

  3. Cima, J.A., Schober, G.: Analytic functions with bounded mean oscillation and logarithms ofH p-functions. Math. Z.151, 295–300 (1976)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  5. Fefferman, C., Stein, E.M.:H p spaces of several variables. Acta Math.129, 137–193 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ferrand, J.: Etude de la correspondence entre les frontières dans la représentation conforme. Bull. Soc. Math. France70, 143–174 (1942)

    MathSciNet  MATH  Google Scholar 

  7. Gattegno, C., Ostrowski, A.: Représentation conforme à la frontière; domaines généraux. Mém. Sci. Math.109, 1949

  8. Cattegno, C., Ostrowski, A.: Représentation conforme à la frontière; domaines particuliers. Mém. Sci. Math.110, 1949

  9. John, F., Nirenberg, L.: On functions of bounded mean oscillation. Comm. Pure Appl. Math.14, 415–426 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lavrent'ev, M.: Boundary problems in the theory of univalent functions (Russian). Mat. Sb. (N.S.)1, 815–844 (1936); Amer. Math. Soc. Translations Ser. 2,32, 1–35 (1963)

    MATH  Google Scholar 

  11. Lehto, O., Virtanen, K.I.: Quasikonforme Abbildungen. Berlin, Heidelberg, New York: Springer 1965

    MATH  Google Scholar 

  12. McMillan, J.E.: Boundary behavior of a conformal mapping. Acta Math.123, 43–67 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  13. McMillan, J.E., Pommerenke, Ch.: On the boundary behavior of analytic functions without Koebe arcs. Math. Ann.189, 275–279 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  14. Neri, U.: Fractional integration on the spaceH 1 and its dual. Studia Math.53, 175–189 (1975)

    MathSciNet  MATH  Google Scholar 

  15. Ostrowski, A.: Zur Randverzerrung bei konformer Abbildung. Prace Mat. Fisycz.44, 371–471 (1936)

    Google Scholar 

  16. Pommerenke, Ch.: Linear-invariante Familien analytischer Funktionen. II. Math. Ann.156, 226–262 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  17. Pommerenke, Ch.: On Bloch functions. J. London Math. Soc.2, 689–695 (1970)

    MathSciNet  MATH  Google Scholar 

  18. Pommerenke, Ch.: Univalent functions. Göttingen: Vandenhoeck & Ruprecht 1975

    MATH  Google Scholar 

  19. Pommerenke, Ch.: Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation. Comm. Math. Helv.52, 591–602 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  20. Sarason, D.: Functions of vanishing mean oscillation. Trans. Amer. Math. Soc.207, 391–405 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  21. Taylor, A.E.: Banach spaces of functions analytic in the unit circle. I. Studia Math.11, 145–170 (1950)

    MathSciNet  MATH  Google Scholar 

  22. Walsh, J.L., Gaier, D.: Zur Methode der variablen Gebiete bei der Randverzerrung. Arch. Math.6, 77–86 (1955)

    Article  MathSciNet  Google Scholar 

  23. Warschawski, S.E.: Zur Randverzerrung bei konformer Abbildung. Compos. Math.1, 314–330 (1935)

    MathSciNet  MATH  Google Scholar 

  24. Warschawski, S.E.: On Hölder continuity at the boundary in conformal maps. J. Math. Mech.18, 423–427 (1968/69)

    MathSciNet  Google Scholar 

  25. Warschawski, S.E., Schober, G.E.: On conformal mapping of certain classes of Jordan domains. Arch. Rational Mech. Anal.22, 201–209 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  26. Visser, C.: Über beschränkte analytische Funktionen und die Randverhältnisse bei konformen Abbildungen. Math. Ann.107, 28–39 (1933)

    Article  MathSciNet  Google Scholar 

  27. Zygmund, A.: Trigonometric series, Vol. I, 2nd ed. Cambridge, MA: Cambridge University Press 1968

    Google Scholar 

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Pommerenke, C. On univalent functions, Bloch functions and VMOA. Math. Ann. 236, 199–208 (1978). https://doi.org/10.1007/BF01351365

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