Imbedding theorems and relations between best approximations (moduli of continuity) in different metrics

In the first part of the work are established imbedding theorems pertaining to arbitrary classes of functions of a single variable $\varphi(L)$, $L\varphi(L)$, $H_p^{\omega(\delta)}$ and $L^\nu\ln^\beta(1+L)$.
The second part contains estimates for best approximations (moduli of continuity) in different metrics. It is shown that in certain cases these estimates cannot be strengthened.
Bibliography: 14 titles.