Estimates of Schwarzian derivative of holomorphic functions in the disk with restriction on real part |
Pavlov N.A. |
2018, issue 1, P. 90-100 |
Abstract |
Series of theorems, including general theorem, for holomorphic functions in the disk are proven. Estimates include derivatives in boundary points of the disk. |
Keywords: holomorphic functions, Schwarzian derivative, symmetrization |
Download the article (PDF-file) |
References |
[1] Z. Nehari, Conformal mapping, McGraw-Hill Book Co., Inc., New York–Toronto–London, 1952, viii+396 pp. [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. [3] M. Chuaqui, P. Duren, W. Ma, D. Mej?a, D. Minda, B. Osgood, “Schwarzian norms and two-point distortion”, Pacific J. Math., 254:1, (2011), 101–116. [4] G.M Goluzin, Geometricheskaja teorija funkcij kompleksnogo peremennogo, 2-e izd., Nauka, M., 1966, 628 s. [5] W.K Hayman, Multivalent functions, 2nd ed., Cambridge Tracts in Math., v. 110, Cambridge Univ. Press, Cambridge, 1994, xii+263 pp. [6] Dzh. Dzhenkins, Odnolistnye funkcii i konformnye otobrazhenija, IL, M., 1962, 265 s. [7] G.V. Kuz'mina, “Metody geometricheskoj teorii funkcij. I”, Algebra i analiz, 9:3, (1997), 41–103. [8] G.V. Kuz'mina, “Metody geometricheskoj teorii funkcij. II”, Algebra i analiz, 9:5, (1997), 1–50. [9] O. Lehto, Univalent functions and Teichmuller spaces, Grad. Texts in Math., v. 109, Springer-Verlag, New York, 1987, xii+257 pp. [10] J. B. Garnett, D.E. Marshall, Harmonic measure, New Math. Monogr., v. 2, Cambridge Univ. Press, Cambridge, 2005, xvi+571 pp. [11] V.N. Dubinin, “O granichnyh znachenijah proizvodnoj SHvarca reguljarnoj funkcii”, Matem. sb., 202:5, (2011), 29–44. [12] V.N. Dubinin, Condenser capacities and symmetrization in geometric function theory, Springer, Basel, 2014, xii+344 pp. [13] V.I. Lavrik, V.N. Savenkov, Spravochnik po konformnym otobrazhenijam, Naukova dumka, Kiev, 1970, 252 s. |