Geodesic
Differential and smoothness properties of continuous functions
Matematičeskie zametki, Tome 22 (1977) no. 6, pp. 785-794

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Necessary and sufficient conditions on functions $\varphi$ and $\psi$ are found in order for the classes of functions $W^rH_\varphi^k$ and $H_\omega^{+k}$ to coincide ($k$ and $r$ are natural numbers). These results are generalizations of [1–4]. 
@article{MZM_1977_22_6_a0,
     author = {E. G. Guseinov and N. A. Il'yasov},
     title = {Differential and smoothness properties of continuous functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {785--794},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_6_a0/}
}
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E. G. Guseinov; N. A. Il'yasov. Differential and smoothness properties of continuous functions. Matematičeskie zametki, Tome 22 (1977) no. 6, pp. 785-794. http://geodesic.mathdoc.fr/item/MZM_1977_22_6_a0/