On the Schwarzian norm of harmonic mappings

S. Yu. Graf

Problemy analiza, Tome 5 (2016) no. 2, pp. 20-32.

Résumé

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.

Détail

Keywords: harmonic mappings; linear invariant families; Schwarzian derivative.

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