On a class of summability methods for multiple Fourier series

The paper shows that the same properties which hold for the classical $(C,1)$-means are preserved for a sufficiently large class of summability methods for multiple Fourier series involving rectangular partial sums. More precisely, Fourier series of continuous functions are uniformly summable by these methods, and Fourier series of functions from the class $L (\ln^+ L)^{m-1}(T^m)$ are summable almost everywhere.
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