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 \(S_{H}^{o}(S)=\{h+\overline{g} \in S_{H}^{o}: \;\ h+e^{i\theta}g \in S\; {\rm for\; some} \; \theta \in \mathbb{R}\}\) and \(K_{H}^{0}(K)=\{h+\overline{g}\in K_{H}^{0}: \; h+e^{i\theta}g\in K \;\ {\rm for\;\ some} \;\ \theta\in \mathbb{R}\}\) 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.