Geodesic
The approximation of a Hölder class of two variables by Riesz spherical means
Matematičeskie zametki, Tome 15 (1974) no. 1, pp. 33-43 
B. I. Golubov. The approximation of a Hölder class of two variables by Riesz spherical means. Matematičeskie zametki, Tome 15 (1974) no. 1, pp. 33-43. http://geodesic.mathdoc.fr/item/MZM_1974_15_1_a3/
@article{MZM_1974_15_1_a3,
     author = {B. I. Golubov},
     title = {The approximation of {a~H\"older} class of two variables by {Riesz} spherical means},
     journal = {Matemati\v{c}eskie zametki},
     pages = {33--43},
     year = {1974},
     volume = {15},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_1_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For periodic functions of the Hölder class $H_2^\alpha$ ($0<\alpha\le1$) defined in the two-dimensional space $E_2$, we find the asymptotic form as $R\to+\infty$ of the quantity $$\sup_{f\in H_2^\alpha}\|S_r^\delta(x,f)-f(x)\|_{C(E_2)}\left(\delta>\frac12+\alpha\right),$$ where $S_R^\delta(x,f)$ is the Riesz spherical mean of order $\delta$ of the Fourier series of the function $f(x)$.