Geodesic
A connection between inclusion theorems and the uniform convergence of multiple Fourier series
Matematičeskie zametki, Tome 12 (1972) no. 2, pp. 139-148.

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A relation is established between inclusion theorems and the uniform convergence of Fourier series for the case of functions of many variables. The one-dimensional case has already been analyzed by Ul'yanov. 
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     author = {N. Temirgaliev},
     title = {A connection between inclusion theorems and the uniform convergence of multiple {Fourier} series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {139--148},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a3/}
}
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N. Temirgaliev. A connection between inclusion theorems and the uniform convergence of multiple Fourier series. Matematičeskie zametki, Tome 12 (1972) no. 2, pp. 139-148. http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a3/