Moduli of smoothness of conformal transformations

P. M. Tamrazov, Smoothness and Polynomial Approximations [in Russian], Naukova Dumka, Kiev (1975). P. M. Tamrazov, “Finite difference moduli of smoothness and polynomial approximations,” Preprint IM-75-10, 24, Kiev (1975). A. O. Gel'fond, The Calculus of Finite Differences [in Russian], Fizmatgiz, Moscow (1967). O. D. Kellog, “Harmonic functions and Green's integral,” Trans. Am. Math. Soc.,13, 109–132 (1912). S. E. Warschawski, “Über ein Satz von O. D. Kellog,” Nach. Ges. Wiss., Göttingen, No. 1, 73–86 (1932). Ya. L. Geronimus, “On some properties of functions continuous in a closed disk,” Dokl. Akad. Nauk SSSR,98, No. 6, 861–889 (1954). S. E. Warschawski, “On differentiability at the boundary in conformal mappings,” Proc. Am. Math. Soc.,12, No. 4, 614–620 (1961). Ou So-mo, “On some boundary properties of conformal mappings,” Sci. Sinica,7, No. 2, 131–136 (1958). S. Ya. Al'per, “On uniform approximations of functions of a complex variable in closed domains,” Izv. Akad. Nauk SSSR, Ser. Mat.,19, No. 6, 423–444 (1955). R. N. Koval'chuk, “A generalization of Kellog's theorem,” Ukr. Mat. Zh.,7, No. 4, 104–108 (1965). L. I. Kolesnik, “Converse of a theorem of Kellog type,” Ukr. Mat. Zh.,21, No. 1, 104–108 (1969). E. V. Karupu, “On finite difference moduli of smoothness for conformal transformations,” Preprint IM-77-6, 12, Kiev (1977). E. V. Karupu, “Moduli of smoothness of conformal homeomorphisms,” Preprint IM-77-11, 12, Kiev (1977). M. F. Timan, Theory of Approximation of Functions of a Real Variable, Pergamon (1963). G. M. Goluzin, The Geometric Theory of Functions of a Complex Variable [in Russian], Fizmatgiz, Moscow (1966). N. K. Bari and S. B. Stechkin, “Best approximations and differential properties of two conjugate functions,” Tr. Mosk. Mat. O-va,5, 483–522 (1956). P. M. Tamrazov, “Finite difference identities and estimates for the moduli of smoothness of a composition of functions,” Preprint IM-77-5, 24, Kiev (1977). R. M. Trigub, “Approximation of functions with a given modulus of smoothness on the exterior of a segment and semiaxis,” in: Studies in Current Problems of Constructive Function Theory [in Russian], Fizmatgiz, Moscow (1961), pp. 47–51. P. M. Tamrazov, “Contour and solid properties of holomorphic functions in a complex domain,” Dokl. Akad. Nauk SSSR,204, No. 3, 565–568 (1972).