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Proceedings of the American Mathematical Society

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Non-Smirnov domains


Author: Knut Øyma
Journal: Proc. Amer. Math. Soc. 123 (1995), 1425-1429
MSC: Primary 30C20
DOI: https://doi.org/10.1090/S0002-9939-1995-1264827-7
MathSciNet review: 1264827
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Abstract: If $ \Omega $ is a Jordan domain, a small perturbation of the boundary gives a non-Smirnov domain.


References [Enhancements On Off] (What's this?)

  • [1] E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999
  • [2] Peter L. Duren, Theory of 𝐻^{𝑝} spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
  • [3] P. L. Duren, H. S. Shapiro, and A. L. Shields, Singular measures and domains not of Smirnov type, Duke Math. J. 33 (1966), 247–254. MR 0199359
  • [4] John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
  • [5] M. W. Keldysh and M. A. Lavrentiev, Sur la représentation conforme des domaines limités par des courbes rectifiables, Ann. Sci. École Norm. Sup. 54 (1937), 1-38.
  • [6] I. I. Priwalow, Randeigenschaften analytischer Funktionen, Zweite, unter Redaktion von A. I. Markuschewitsch überarbeitete und ergänzte Auflage. Hochschulbücher für Mathematik, Bd. 25, VEB Deutscher Verlag der Wissenschaften, Berlin, 1956 (German). MR 0083565

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1264827-7
Article copyright: © Copyright 1995 American Mathematical Society