Geodesic
The best approximation of the differentiation operator in the metric of~$L_p$
Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 531-538.

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For Stechkin's problem of the best approximation for the differentiation operator $$ E_n=\inf_{\substack{L_q\\ ||V||_{L_p}\leqslant n}}\sup_{||f^{(l)}||_{L_r(S)}\leqslant 1}||f^{(k)}-Vf||_{L_q(S)} $$ we indicate the necessary and sufficient conditions that $E_n$ be finite. We study some properties of continuous linear operators $V$ from $L_p$ into $L_q$. 
@article{MZM_1972_12_5_a4,
     author = {V. N. Gabushin},
     title = {The best approximation of the differentiation operator in the metric of~$L_p$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {531--538},
     publisher = {mathdoc},
     volume = {12},
     number = {5},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a4/}
}
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V. N. Gabushin. The best approximation of the differentiation operator in the metric of~$L_p$. Matematičeskie zametki, Tome 12 (1972) no. 5, pp. 531-538. http://geodesic.mathdoc.fr/item/MZM_1972_12_5_a4/