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Matematicheskie Zametki, 2010, Volume 87, Issue 4, Pages 492–501
DOI: https://doi.org/10.4213/mzm8368 (Mi mzm8368) 		 
On the Convergence in Mean of Trigonometric Fourier Series

A. S. Belov

Ivanovo State University
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DOI: https://doi.org/10.4213/mzm8368
Abstract: 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, Abel transformation, Dirichlet kernel.
Received: 14.01.2009
English version:
Mathematical Notes, 2010, Volume 87, Issue 4, Pages 466–474
DOI: https://doi.org/10.1134/S0001434610030247
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: A. S. Belov, “On the Convergence in Mean of Trigonometric Fourier Series”, Mat. Zametki, 87:4 (2010), 492–501; Math. Notes, 87:4 (2010), 466–474
Citation in format AMSBIB
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