Geodesic
Necessary and sufficient conditions for the imbedding of some classes of functions
Izvestiya. Mathematics, Tome 7 (1973) no. 2, pp. 388-400 
È. A. Storozhenko. Necessary and sufficient conditions for the imbedding of some classes of functions. Izvestiya. Mathematics, Tome 7 (1973) no. 2, pp. 388-400. http://geodesic.mathdoc.fr/item/IM2_1973_7_2_a8/
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     title = {Necessary and sufficient conditions for the imbedding of some classes of functions},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions are found for membership of a function $f(x)\in L^p(0,1)$ in the class $L^q\Phi (L)$, $1\le p\le q\infty$. A connection is established between the modulus of continuity $\omega(\delta,f^*)$ and, on the one hand, the Fourier coefficients $a_n(f^*)$ and $b_n(f^*)$, and on the other hand the modulus of continuity $\omega(\delta,f)$.

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