Estimates for Holomorphic Functions with Values in C\{0,1}
Author(s)
P. V. Dovbush*
Affiliation(s)
Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Kishinev, Republic of Moldova.
Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Kishinev, Republic of Moldova.
ABSTRACT
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.
Cite this paper
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.
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.
References
[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. http://portail.mathdoc.fr/JMPA/afficher_notice.php?id=JMPA_1929_9_8_A10_0 [2] P. V. Dovbush, “On a Normality Criterion of S. Mandelbrojt,” 2013. http://arxiv.org/abs/1302.1695 [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
[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. http://portail.mathdoc.fr/JMPA/afficher_notice.php?id=JMPA_1929_9_8_A10_0 [2] P. V. Dovbush, “On a Normality Criterion of S. Mandelbrojt,” 2013. http://arxiv.org/abs/1302.1695 [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