ON THE SCHWARZIAN NORM OF HARMONIC MAPPINGS

Проблемы анализа

S. Yu. Graf¹ 

[1] Tver State University;

关键词: harmonic mappings;    linear invariant families;    Schwarzian derivative;   

DOI  :  10.15393/j3.art.2016.3511

来源: DOAJ

【 摘 要 】

We obtain estimations of the pre-Schwarzian and Schwarzian derivatives in terms of the order of family in linear and affine invariant families L of sense preserving harmonic mappings of the unit disk D. As the converse result the order of family L is estimated in terms of suprema of Schwarzian and pre-Schwarzian norms over the family L. Main results are obtained by means of theory of linear invariant families.

【 授权许可】

Unknown