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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V. I. Smirnov, “Sur la théorie des polynômes orthogonaux à la variable complexe,” Zh. Leningr. Fiz.-Mat. Ob-va,2, 155–179 (1928).
G. Ts. Tumarkin, “On a sufficient condition for a domain to belong to the class S,” Vestnik Leningrad. Gos. Univ.,13, 47–55 (1962).
D. Blackwell and D. Freedman, “On the amount of variance needed to escape from a strip,” Ann. Probab.,1, No. 5, 772–787 (1973).
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).
D. S. Jerison and C. E. Kenig, “Hardy spaces, H∞ and singular integrals on chord-arc domains,” Math. Scand.,50, 221–247 (1982).
J.-P. Kahane, “Trois notes sur les ensembles parfaits linéaires,” Enseign. Math.,15, 185–192 (1969).
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).
T. L. Lai, “First exit times from moving boundaries for sums of independent random variables,” Ann. Probab.,5, No. 2, 210–221 (1977).
N. G. Makarov, “Conformal mapping and Hausdorff measures,” Ark. Mat.25, No. 1, 41–89 (1987).
N. G. Makarov, LIL for smooth measures. LOMI Preprint E-3-88 (1988).
H. S. Shapiro, “Remarks concerning domains of Smirnov type,” Michigan Math. J.,13, 341–348 (1966).
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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