Distortion theorem for bounded univalent functions
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 238-246 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2015},
     volume = {15},
     number = {2},
     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
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
%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