Geodesic
On the Schwarzian norm of harmonic mappings
Problemy analiza, Tome 5 (2016) no. 2, pp. 20-32

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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. 
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     author = {S. Yu. Graf},
     title = {On the {Schwarzian} norm of harmonic mappings},
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     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2016_5_2_a1/}
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S. Yu. Graf. On the Schwarzian norm of harmonic mappings. Problemy analiza, Tome 5 (2016) no. 2, pp. 20-32. http://geodesic.mathdoc.fr/item/PA_2016_5_2_a1/