Geodesic
Linear summation methods and the absolute convergence of Fourier series
Izvestiya. Mathematics , Tome 2 (1968) no. 1, pp. 21-46.

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We establish a connection between the summability and the absolute convergence of Fourier series and apply it in both directions. 
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R. M. Trigub. Linear summation methods and the absolute convergence of Fourier series. Izvestiya. Mathematics , Tome 2 (1968) no. 1, pp. 21-46. http://geodesic.mathdoc.fr/item/IM2_1968_2_1_a1/

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