Geodesic
Imbedding theorems and relations between best approximations (moduli of continuity) in different metrics
Sbornik. Mathematics, Tome 10 (1970) no. 1, pp. 103-126

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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. 
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     author = {P. L. Ul'yanov},
     title = {Imbedding theorems and relations between best approximations (moduli of continuity) in different metrics},
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P. L. Ul'yanov. Imbedding theorems and relations between best approximations (moduli of continuity) in different metrics. Sbornik. Mathematics, Tome 10 (1970) no. 1, pp. 103-126. http://geodesic.mathdoc.fr/item/SM_1970_10_1_a7/