Geodesic
A generalization of a theorem of Marcinkiewicz
Izvestiya. Mathematics , Tome 2 (1968) no. 5, pp. 1065-1075

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It is proved that a double Fourier series is $(C,\alpha)$-summable with $\alpha>0$ almost everywhere. 
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     author = {L. V. Zhizhiashvili},
     title = {A generalization of a theorem of {Marcinkiewicz}},
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L. V. Zhizhiashvili. A generalization of a theorem of Marcinkiewicz. Izvestiya. Mathematics , Tome 2 (1968) no. 5, pp. 1065-1075. http://geodesic.mathdoc.fr/item/IM2_1968_2_5_a6/