Geodesic
Approximation of classes of differentiable functions
Matematičeskie zametki, Tome 9 (1971) no. 2, pp. 105-112

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Conditions are derived under which $$ F=\sup_{||f^{(k)}||_{L_p(S)}\leqslant1}\,\inf_{||\varphi^{(l)}||_{L_r(S)}\leqslant n}||f-\varphi||_{L_p(S)} $$ is finite or infinite. The value of $F$ is calculated for certain special cases. 
@article{MZM_1971_9_2_a0,
     author = {V. V. Arestov and V. N. Gabushin},
     title = {Approximation of classes of differentiable functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {105--112},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_2_a0/}
}
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V. V. Arestov; V. N. Gabushin. Approximation of classes of differentiable functions. Matematičeskie zametki, Tome 9 (1971) no. 2, pp. 105-112. http://geodesic.mathdoc.fr/item/MZM_1971_9_2_a0/