The conditions for the imbedding of the classes $H^\omega_{k,\,R}$ и $\widetilde H^\omega_{k,\,R}$

We find the necessary and sufficient conditions for the imbeddings $H^\omega_{l,R}\subset H^\varphi_{k,R}, H^\omega_{l,R}\subset\widetilde H^\varphi_{k,R}$ in terms of the majorants $\omega$ and $\varphi(R=L_{2\pi},C_{2\pi};l>k)$.