Geodesic
Approximation of functions from $B^\ell_{p,\theta}(G)$ by anisotropic averages
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 80 (1978), pp. 30-47

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The article considers the approximation of functions from O. V. Besov's class $B^\ell_{p,\theta}(G)$ by anisotropic average functions. Proofs are given of the approximation theorem, the inverse theorem of approximation theory, and the saturation theorem associated with the choice of the averaging kernel. 
@article{ZNSL_1978_80_a1,
     author = {V. P. Il'in},
     title = {Approximation of functions from $B^\ell_{p,\theta}(G)$ by anisotropic averages},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {30--47},
     publisher = {mathdoc},
     volume = {80},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a1/}
}
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%F ZNSL_1978_80_a1
V. P. Il'in. Approximation of functions from $B^\ell_{p,\theta}(G)$ by anisotropic averages. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 80 (1978), pp. 30-47. http://geodesic.mathdoc.fr/item/ZNSL_1978_80_a1/