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Size of the set of singular points on the boundary of a non-Smirnov domain

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Abstract

One improves the necessary conditions of G. Ts. Tumarkin and H. Shapiro for a Jordan domain to belong to the Smirnov class.

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Literature cited

  1. V. I. Smirnov, “Sur la théorie des polynômes orthogonaux à la variable complexe,” Zh. Leningr. Fiz.-Mat. Ob-va,2, 155–179 (1928).

    Google Scholar 

  2. G. Ts. Tumarkin, “On a sufficient condition for a domain to belong to the class S,” Vestnik Leningrad. Gos. Univ.,13, 47–55 (1962).

    Google Scholar 

  3. D. Blackwell and D. Freedman, “On the amount of variance needed to escape from a strip,” Ann. Probab.,1, No. 5, 772–787 (1973).

    Google Scholar 

  4. P. L. Duren, H. S. Shapiro, and A. L. Shields, “Singular measures and domains not of Smirnov type,” Duke Math. J.,33, No. 2, 247–254(1966).

    Google Scholar 

  5. D. S. Jerison and C. E. Kenig, “Hardy spaces, H and singular integrals on chord-arc domains,” Math. Scand.,50, 221–247 (1982).

    Google Scholar 

  6. J.-P. Kahane, “Trois notes sur les ensembles parfaits linéaires,” Enseign. Math.,15, 185–192 (1969).

    Google Scholar 

  7. M. V. Keldys and M. A. Lavrentiev, “Sur la représentation conforme des domaines limités par des courbes rectifiables,” Ann. Sci. Ecole Norm. Sup.,54, 1–38 (1937).

    Google Scholar 

  8. T. L. Lai, “First exit times from moving boundaries for sums of independent random variables,” Ann. Probab.,5, No. 2, 210–221 (1977).

    Google Scholar 

  9. N. G. Makarov, “Conformal mapping and Hausdorff measures,” Ark. Mat.25, No. 1, 41–89 (1987).

    Google Scholar 

  10. N. G. Makarov, LIL for smooth measures. LOMI Preprint E-3-88 (1988).

  11. H. S. Shapiro, “Remarks concerning domains of Smirnov type,” Michigan Math. J.,13, 341–348 (1966).

    Google Scholar 

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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 176–183, 1989.

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Makarov, N.G. Size of the set of singular points on the boundary of a non-Smirnov domain. J Math Sci 63, 212–216 (1993). https://doi.org/10.1007/BF01099312

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  • DOI: https://doi.org/10.1007/BF01099312

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