Geodesic
On the Convergence in Mean of Trigonometric Fourier Series
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 492-501

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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 
@article{MZM_2010_87_4_a1,
     author = {A. S. Belov},
     title = {On the {Convergence} in {Mean} of {Trigonometric} {Fourier} {Series}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {492--501},
     publisher = {mathdoc},
     volume = {87},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a1/}
}
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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/