|
This article is cited in 8 scientific papers (total in 8 papers)
On the Schwarzian norm of harmonic mappings
S. Yu. Grafab a Petrozavodsk State University, 33, Lenina st., 185910 Petrozavodsk, Russia
b Tver State University, 33, Zheliabova st., 170100 Tver, Russia
Abstract:
We obtain estimations of the pre-Schwarzian and Schwarzian derivatives in terms of the order of family in linear and affine invariant families $\mathcal{L}$ of sense preserving harmonic mappings of the unit disk $\mathbb{D}$. As the converse result the order of family $\mathcal{L}$ is estimated in terms of suprema of Schwarzian and pre-Schwarzian norms over the family $\mathcal{L}$. Main results are obtained by means of theory of linear invariant families.
Keywords:
harmonic mappings; linear invariant families; Schwarzian derivative.
Received: 19.10.2016 Revised: 11.12.2016 Accepted: 13.12.2016
Citation:
S. Yu. Graf, “On the Schwarzian norm of harmonic mappings”, Probl. Anal. Issues Anal., 5(23):2 (2016), 20–32
Linking options:
https://www.mathnet.ru/eng/pa199 https://www.mathnet.ru/eng/pa/v23/i2/p20
|
Statistics & downloads: |
Abstract page: | 225 | Full-text PDF : | 75 | References: | 24 |
|