Geodesic
The imbedding and equality of certain classes of functions
Izvestiya. Mathematics , Tome 3 (1969) no. 4, pp. 795-813

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This paper is concerned with the interrelation of certain conditions expressed in terms of best approximations, moduli of smoothness, $k$th differences of the functions in question, or the inclusion in $L_p$ of the transformed Fourier series. 
@article{IM2_1969_3_4_a5,
     author = {M. K. Potapov},
     title = {The imbedding and equality of certain classes of functions},
     journal = {Izvestiya. Mathematics },
     pages = {795--813},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_4_a5/}
}
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M. K. Potapov. The imbedding and equality of certain classes of functions. Izvestiya. Mathematics , Tome 3 (1969) no. 4, pp. 795-813. http://geodesic.mathdoc.fr/item/IM2_1969_3_4_a5/