Growth and Distortion Theorems for Some Univalent Harmonic Mappings

Let $S$ and $K$ denote the usual classes of normalized univalent analytic and normalized convex analytic functions, respectively. Similarly, let $S_H^0$ and $K_H^0$, respectively, denote these classes in the harmonic case. It is known that the classes $S_H^o(S)=\{h+\bar{g}\in S_H^o:h+e^{i\theta }g\in S\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{o}\mathrm{m}\mathrm{e}\theta \in \mathbb{R}\}$ and $K_H^0(K)=\{h+\bar{g}\in K_H^0:h+e^{i\theta }g\in K\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{s}\mathrm{o}\mathrm{m}\mathrm{e}\theta \in \mathbb{R}\}$ are, respectively, subclasses of normalized univalent harmonic and normalized convex harmonic functions. We give estimates of some functionals defined on the functions of these classes.