Geodesic
Estimates of Schwarzian derivative of holomorphic functions in the disk with restriction on real part
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 1, pp. 90-100 
N. A. Pavlov. Estimates of Schwarzian derivative of holomorphic functions in the disk with restriction on real part. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 1, pp. 90-100. http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a11/
@article{DVMG_2018_18_1_a11,
     author = {N. A. Pavlov},
     title = {Estimates of {Schwarzian} derivative of holomorphic functions in the disk with restriction on real part},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {90--100},
     year = {2018},
     volume = {18},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a11/}
}
TY  - JOUR
AU  - N. A. Pavlov
TI  - Estimates of Schwarzian derivative of holomorphic functions in the disk with restriction on real part
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2018
SP  - 90
EP  - 100
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a11/
LA  - ru
ID  - DVMG_2018_18_1_a11
ER  - 
%0 Journal Article
%A N. A. Pavlov
%T Estimates of Schwarzian derivative of holomorphic functions in the disk with restriction on real part
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2018
%P 90-100
%V 18
%N 1
%U http://geodesic.mathdoc.fr/item/DVMG_2018_18_1_a11/
%G ru
%F DVMG_2018_18_1_a11

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

Series of theorems, including general theorem, for holomorphic functions in the disk are proven. Estimates include derivatives in boundary points of the disk.

[1] Z. Nehari, Conformal mapping, McGraw-Hill Book Co., Inc., New York–Toronto–London, 1952, viii+396 pp. | MR | Zbl

[2] B. Osgood, “Old and new on the Schwarzian derivative”, Quasiconformal mappings and analysis, A collection of papers honoring Frederick W. Gehring to his 70th birthday (Ann Arbor, MI, August 1995), Springer, New York, 1998, 275–308 | MR | Zbl

[3] M. Chuaqui, P. Duren, W. Ma, D. Mejía, D. Minda, B. Osgood, “Schwarzian norms and two-point distortion”, Pacific J. Math., 254:1 (2011), 101–116 | DOI | MR | Zbl

[4] G. M Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, 2-e izd., Nauka, M., 1966, 628 pp. | MR

[5] W. K Hayman, Multivalent functions, 2nd ed., Cambridge Tracts in Math., v. 110, Cambridge Univ. Press, Cambridge, 1994, xii+263 pp. | MR | Zbl

[6] Dzh. Dzhenkins, Odnolistnye funktsii i konformnye otobrazheniya, IL, M., 1962, 265 pp.

[7] G. V. Kuzmina, “Metody geometricheskoi teorii funktsii. I”, Algebra i analiz, 9:3 (1997), 41–-103 | Zbl

[8] G. V. Kuzmina, “Metody geometricheskoi teorii funktsii. II”, Algebra i analiz, 9:5 (1997), 1–-50 | Zbl

[9] O. Lehto, Univalent functions and Teichmüller spaces, Grad. Texts in Math., v. 109, Springer-Verlag, New York, 1987, xii+257 pp. | MR | Zbl

[10] J. B. Garnett, D. E. Marshall, Harmonic measure, New Math. Monogr., v. 2, Cambridge Univ. Press, Cambridge, 2005, xvi+571 pp. | MR | Zbl

[11] V. N. Dubinin, “O granichnykh znacheniyakh proizvodnoi Shvartsa regulyarnoi funktsii”, Matem. sb., 202:5 (2011), 29–44 | DOI | MR | Zbl

[12] V. N. Dubinin, Condenser capacities and symmetrization in geometric function theory, Springer, Basel, 2014, xii+344 pp. | MR | Zbl

[13] V. I. Lavrik, V. N. Savenkov, Spravochnik po konformnym otobrazheniyam, Naukova dumka, Kiev, 1970, 252 pp. | MR