Geodesic
Exact inequalities for the upper bounds of seminorms on a class of periodic functions
Matematičeskie zametki, Tome 13 (1973) no. 5, pp. 647-654 Cet article a éte moissonné depuis la source Math-Net.Ru

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We establish exact inequalities for the upper bounds of seminorms on classes of differentiable periodic functions, and as corollaries of them, exact inequalities between the best approximations by trigonometric polynomials of functions and their derivatives in the metrics of $C$ and $L$. 
@article{MZM_1973_13_5_a2,
     author = {A. A. Ligun},
     title = {Exact inequalities for the upper bounds of seminorms on a~class of periodic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {647--654},
     year = {1973},
     volume = {13},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_5_a2/}
}
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A. A. Ligun. Exact inequalities for the upper bounds of seminorms on a class of periodic functions. Matematičeskie zametki, Tome 13 (1973) no. 5, pp. 647-654. http://geodesic.mathdoc.fr/item/MZM_1973_13_5_a2/