On the Schwarzian norm of harmonic mappings

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.