Estimates for Holomorphic Functions with Values in C\{0,1} ()
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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
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
|