REFERENCES
O. D. Kellogg, "Harmonic functions and Green's integral," Trans. Amer. Math. Soc., 13, 109-132 (1912).
S. E. Warschawski, "On the higher derivatives at the boundary in conformal mappings," Trans. Amer. Math. Soc. 38, No. 2, 310-340 (1935).
P. M. Tamrazov, "Contour and solid structure properties of holomorphic functions of a complex variable," Usp. Mat. Nauk, 28, No. 1, 131-161 (1973); English translation: Russian Math. Surveys 28, 141-173 (1973).
M. A. Lavrent'ev, "On continuity of univalent functions on closed domains," Dokl. Akad. Nauk SSSR, 4, No. 5, 207-209 (1936).
S. E. Warschawski, "On differentiability at the boundary in conformal mappings," Proc. Amer. Math. Soc., 12, No. 4, 614-620 (1961).
E. P. Dolzhenko, "Some remarks on the modulus of continuity of a conformal mapping onto a Jordan domain," Math. Notes, 60, No. 2, 176-184 (1996).
P. S. Urysohn, "The relation between the mean width and volume of convex bodies in n-dimensional space," Mat. Sb., 31, 477-486 (1924).
L. Ahlfors, Lectures on Quasiconformal Mappings, Princeton Univ. Press, Princeton, (1966).
E. P. Dolzhenko, "On conformal mappings of Jordan domains," Vestn. MGU, Mat., Mekh., No. 3, 66-68 (1999); English translation: Moscow Univ. Math. Bull., 54 (1999).
I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], GITTL, Moscow-Leningrad (1950); German translation: Randeigenschaften analytischer Funktionen, Berlin, Dt. Verl. d.Wiss. (1956).
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Dolzhenko, E.P. On Modules of Continuity of Conformal Mappings of Arbitrary Jordan Domains. Journal of Mathematical Sciences 108, 411–419 (2002). https://doi.org/10.1023/A:1012858101181
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DOI: https://doi.org/10.1023/A:1012858101181