Geodesic
Embedding of $H_p^\omega$ in the class $e^L$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 3-8

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We obtain the necessary conditions for the embedding $H_p^\omega\subset e^L$ ($1\le p\infty$) with convex modulus of continuity $\omega$ in terms of this modulus. In the case $p=1$ these conditions are also sufficient.
Keywords: modulus of continuity, decreasing rearrangement, embedding in the class $\varphi(L)$. 
@article{IVM_2010_3_a0,
     author = {V. A. Andrienko},
     title = {Embedding of $H_p^\omega$ in the class $e^L$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--8},
     publisher = {mathdoc},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_3_a0/}
}
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V. A. Andrienko. Embedding of $H_p^\omega$ in the class $e^L$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2010), pp. 3-8. http://geodesic.mathdoc.fr/item/IVM_2010_3_a0/