Geodesic
On the convergence of Riesz spherical means of multiple Fourier series and integrals of functions of bounded generalized variation
Sbornik. Mathematics, Tome 18 (1972) no. 4, pp. 635-658 
B. I. Golubov. On the convergence of Riesz spherical means of multiple Fourier series and integrals of functions of bounded generalized variation. Sbornik. Mathematics, Tome 18 (1972) no. 4, pp. 635-658. http://geodesic.mathdoc.fr/item/SM_1972_18_4_a6/
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     author = {B. I. Golubov},
     title = {On~the convergence of {Riesz} spherical means of multiple {Fourier} series and integrals of functions of bounded generalized variation},
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     volume = {18},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1972_18_4_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A necessary and sufficient condition is found for the pointwise convergence of the Riesz spherical means of critical order of multiple Fourier series and integrals in the class of functions whose spherical Steklov means at the given point have (as a function of the radius of the sphere) bounded generalized variation. Bibliography: 25 titles.

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