Geodesic
Hilbert--Schmidt operators and the absolute convergence of fourier series
Izvestiya. Mathematics , Tome 4 (1970) no. 1, pp. 215-223.

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Sufficient conditions are proved for integral operators to belong to ideals of the ring of operators; applications of the results obtained to the question of absolute convergence of Fourier series are given. 
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S. L. Blyumin; B. D. Kotlyar. Hilbert--Schmidt operators and the absolute convergence of fourier series. Izvestiya. Mathematics , Tome 4 (1970) no. 1, pp. 215-223. http://geodesic.mathdoc.fr/item/IM2_1970_4_1_a11/

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