Geodesic
Imbedding theorems for the spaces $H_p^{\omega,k}$ and $H_p^{s,\omega,k}$
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part 8, Tome 159 (1987), pp. 83-102

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Imbedding theorems for the spaces $H_p^{\omega,k}$ and $H_p^{s,\omega,k}$, $1$ (with arbitrary smoothness function $\omega$) are studied. In particular, symmetric hulls of these spaces are described, necessary and sufficient conditions of imbedding in Orlicz and Lorentz spaces are derived, and unimprovable bounds of the moduli of continuity in $L_q$, $p$, are given. 
@article{ZNSL_1987_159_a7,
     author = {Yu. V. Netrusov},
     title = {Imbedding theorems for the spaces $H_p^{\omega,k}$ and $H_p^{s,\omega,k}$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {83--102},
     publisher = {mathdoc},
     volume = {159},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_159_a7/}
}
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Yu. V. Netrusov. Imbedding theorems for the spaces $H_p^{\omega,k}$ and $H_p^{s,\omega,k}$. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part 8, Tome 159 (1987), pp. 83-102. http://geodesic.mathdoc.fr/item/ZNSL_1987_159_a7/