Geodesic
Best approximations in $L_[0,infty)$ of the differentiation operator
Matematičeskie zametki, Tome 9 (1971) no. 5, pp. 477-481.

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A solution of Stechkin's problem concerning the approximation in $L_[0,infty)$ of the first-order differentiation operator in the class of functions of arbitrary bounded variation; the exact constant in the inequality $\|f'\|\leqslant K(\|f\|\bigvee\limits_0^\infty f')^{1/2}$ is found. 
@article{MZM_1971_9_5_a0,
     author = {V. I. Berdyshev},
     title = {Best approximations in $L_[0,infty)$ of the differentiation operator},
     journal = {Matemati\v{c}eskie zametki},
     pages = {477--481},
     publisher = {mathdoc},
     volume = {9},
     number = {5},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_5_a0/}
}
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V. I. Berdyshev. Best approximations in $L_[0,infty)$ of the differentiation operator. Matematičeskie zametki, Tome 9 (1971) no. 5, pp. 477-481. http://geodesic.mathdoc.fr/item/MZM_1971_9_5_a0/