Geodesic
The best approximation to a class of functions of several variables by another class and related extremum problems
Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 323-340

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We study the relationship between several extremum problems for unbounded linear operators of convolution type in the spaces $L_\gamma=L_\gamma(\mathbb R^m)$, $m\ge1$, $1\le\gamma\le\infty$. For the problem of calculating the modulus of continuity of the convolution operator $A$ on the function class $Q$ defined by a similar operator and for the Stechkin problem on the best approximation of the operator $A$ on the class $Q$ by bounded linear operators, we construct dual problems in dual spaces, which are the problems on, respectively, the best and the worst approximation to a class of functions by another class. 
@article{MZM_1998_64_3_a0,
     author = {V. V. Arestov},
     title = {The best approximation to a class of functions of several variables by another class and related extremum problems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--340},
     publisher = {mathdoc},
     volume = {64},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a0/}
}
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V. V. Arestov. The best approximation to a class of functions of several variables by another class and related extremum problems. Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 323-340. http://geodesic.mathdoc.fr/item/MZM_1998_64_3_a0/