On some class of functions with an integral representation involving complex measures

In this paper we obtain some properties of functions extremal with respect to Frechet-differentiable functionals defined on $\mathcal{P}'_{\alpha}$ (see defifnition 1) and, in consequence, estimates of the functional $Re\{e^{i\lambda} p(z)\}, 0\ne z\in K, \lambda \in [-\pi, \pi), p\in \mathcal{P}'_{\alpha}$.