Geodesic
On the Convergence in Mean of Trigonometric Fourier Series
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 492-501 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove the sharpness of Zygmund's theorem, which asserts that if a $2\pi$-periodic function $f$ belongs to $L\ln^+ L$, then its Fourier series is convergent in mean.
Keywords: trigonometric Fourier series, $2\pi$-periodic function, convergence in mean, Zygmund's theorem, Dirichlet kernel.
Mots-clés : Abel transformation 
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A. S. Belov. On the Convergence in Mean of Trigonometric Fourier Series. Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 492-501. http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a1/

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