Estimates for Holomorphic Functions with Values in C\{0,1}


Extension of classical Mandelbrojt’s criterion for normality to several complex variables is given. Some inequalities for holomorphic functions which omit values 0 and 1 are obtained.

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P. Dovbush, "Estimates for Holomorphic Functions with Values in C\{0,1}," Advances in Pure Mathematics, Vol. 3 No. 6, 2013, pp. 586-589. doi: 10.4236/apm.2013.36075.

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The authors declare no conflicts of interest.


[1] S. Mandelbrojt, “Sur les Suites de Fonctions Holomorphes. Les Suites Correspondantes des Fonctions Dérivées. Fonctions Entières,” Journal de Mathématiques Pures et Appliquées, Vol. 9, No. 8, 1929, pp. 173-196.
[2] P. V. Dovbush, “On a Normality Criterion of S. Mandelbrojt,” 2013.
[3] W. T. Lai, “The Exact Value of Heyman’s Constant in Landau’s Theorem,”Scientia Sinica, Vol. 22, 1979, pp. 129-133.
[4] E. M. Chirka, “Harnack Inequalities, Kobayashi Distances and Holomorphic Motions,” Proceedings of the Steklov Institute of Mathematics, Vol. 279, No. 1, 2012, pp. 194-206. doi:10.1134/S0081543812080135
[5] J. L. Shiff, “Normal Families,” Springer-Verlag, New York, 1993. doi:10.1007/978-1-4612-0907-2
[6] S. Kobayashi, “Hyperbolic Complex Space,” Springer-Verlag, New York, 1998. doi:10.1007/978-3-662-03582-5

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