Geodesic
Conditions for the localization of partial sums of S.\,M.~Nikol'skii's class of multiple trigonometric Fourier series
Matematičeskie zametki, Tome 8 (1970) no. 5, pp. 595-606

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Best-possible conditions, in S. M. Nikol'skii's classes $H^\alpha_p$, are established for the localization of rectangular (or, as they are sometimes called, Pringsheim) partial sums of multiple trigonometric Fourier series. 
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     author = {V. A. Il'in},
     title = {Conditions for the localization of partial sums of {S.\,M.~Nikol'skii's} class of multiple trigonometric {Fourier} series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {595--606},
     publisher = {mathdoc},
     volume = {8},
     number = {5},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_5_a6/}
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V. A. Il'in. Conditions for the localization of partial sums of S.\,M.~Nikol'skii's class of multiple trigonometric Fourier series. Matematičeskie zametki, Tome 8 (1970) no. 5, pp. 595-606. http://geodesic.mathdoc.fr/item/MZM_1970_8_5_a6/