Линейно-инвариантные семейства, обобщающие $U'_{\alpha}$ и $U^*_{\alpha}$

The idea of linearly invariant families was introduced by Ch. Pommerenke in 1964. In the theory of linearly invariant families the later considered linearly invariant families $U'_{\alpha}$ and $U^*_{\alpha}$ of functions having an integral representation turned out to be especially interesting. In the paper we introduce a new linearly invariant family of functions given by Stieltjes integral. This family is wider than $U'_{\alpha}$ and $U^*_{\alpha}$.