Geodesic
Approximation of continuous periodic functions of many variables by spherical Riesz means
Matematičeskie zametki, Tome 15 (1974) no. 5, pp. 821-832
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We find in succession exact upper bounds for the magnitudes of the least upper bounds of the deviations of spherical Riesz means on classes of continuous periodic functions of many variables and, in a number of cases, we prove the asymptotic exactness of these estimates. 
@article{MZM_1974_15_5_a18,
     author = {A. I. Stepanets},
     title = {Approximation of continuous periodic functions of many variables by spherical {Riesz} means},
     journal = {Matemati\v{c}eskie zametki},
     pages = {821--832},
     year = {1974},
     volume = {15},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_5_a18/}
}
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A. I. Stepanets. Approximation of continuous periodic functions of many variables by spherical Riesz means. Matematičeskie zametki, Tome 15 (1974) no. 5, pp. 821-832. http://geodesic.mathdoc.fr/item/MZM_1974_15_5_a18/