Geodesic
Distortion theorem for bounded univalent functions
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 238-246.

Voir la notice de l'article provenant de la source Math-Net.Ru

Distortion theorem for bounded univalent functions in the unit disk is proven. Estimate includes angular derivatives in two boundary points and Schwarzian derivative in interior point of the unit disk. 
@article{DVMG_2015_15_2_a7,
     author = {N. A. Pavlov},
     title = {Distortion theorem for bounded univalent functions},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {238--246},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a7/}
}
TY  - JOUR
AU  - N. A. Pavlov
TI  - Distortion theorem for bounded univalent functions
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2015
SP  - 238
EP  - 246
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a7/
LA  - ru
ID  - DVMG_2015_15_2_a7
ER  - 
%0 Journal Article
%A N. A. Pavlov
%T Distortion theorem for bounded univalent functions
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2015
%P 238-246
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a7/
%G ru
%F DVMG_2015_15_2_a7
N. A. Pavlov. Distortion theorem for bounded univalent functions. Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 238-246. http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a7/

[1] Ch. Pommerenke, Boundary behaviour of conformal maps, Springer, Berlin, 1992 | MR | Zbl

[2] C. C. Cowen, Ch. Pommerenke, “Inequalities for the angular derivative of an analytic function in the unit disk”, J. London Math. Soc., 2:26 (1982), 271–289 | DOI | MR

[3] A. Frolova, M. Levenshtein, D. Shoikhet, A. Vasil'ev, “Boundary distortion estimates for holomorphic maps”, Complex Analysis and Operator Theory, 8:5 (2014), 1129–1149 | DOI | MR | Zbl

[4] Ch. Pommerenke, A. Vasil'ev, “Angular derivatives of bounded univalent functions and extremal partitions of the unit disk”, Pacific. J. Math., 206:2 (2002), 425–450 | DOI | MR | Zbl

[5] Z. Nehari, “Some inequalities in the theory of functions”, Trans. Amer. Math. Soc., 75:2 (1953), 256–286 | DOI | MR | Zbl

[6] V. N. Dubinin, Emkosti kondensatorov i simmetrizatsiya v geometricheskoi teorii funktsii kompleksnogo peremennogo, Dalnauka, Vladivostok, 2009

[7] I. I. Privalov, Vvedenie v teoriyu funktsii funktsii kompleksnogo peremennogo, Nauka, Glavnaya redaktsiya fiziko-matematicheskoi literatury, M., 1984 | MR