Geodesic
Inequalities for differentiable periodic functions and best approximation of one class of functions by another
Izvestiya. Mathematics , Tome 6 (1972) no. 2, pp. 417-428

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New results are obtained in this paper which elucidate properties of differentiable periodic functions connected with rearrangements. These results are applied in order to obtain a sharp estimate of the best uniform approximation of functions of the class $W^rH_\omega$ by functions of the class $W^{r+1}K$. 
@article{IM2_1972_6_2_a5,
     author = {N. P. Korneichuk},
     title = {Inequalities for differentiable periodic functions and best approximation of one class of functions by another},
     journal = {Izvestiya. Mathematics },
     pages = {417--428},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a5/}
}
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N. P. Korneichuk. Inequalities for differentiable periodic functions and best approximation of one class of functions by another. Izvestiya. Mathematics , Tome 6 (1972) no. 2, pp. 417-428. http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a5/