Geodesic
Strong means and oscillation of multiple Fourier series in multiplicative systems
Matematičeskie zametki, Tome 63 (1998) no. 4, pp. 607-616

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In this paper we establish a general assertion relating the oscillation of the sequence of rectangular partial sums of a multiple Fourier series in a multiplicative system to the strong summability of this series. The systems of group generators are assumed to be uniformly bounded. Earlier these assertions were obtained by the author for the Walsh and Chrestenson series. 
@article{MZM_1998_63_4_a13,
     author = {V. A. Rodin},
     title = {Strong means and oscillation of multiple {Fourier} series in multiplicative systems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {607--616},
     publisher = {mathdoc},
     volume = {63},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_4_a13/}
}
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V. A. Rodin. Strong means and oscillation of multiple Fourier series in multiplicative systems. Matematičeskie zametki, Tome 63 (1998) no. 4, pp. 607-616. http://geodesic.mathdoc.fr/item/MZM_1998_63_4_a13/