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Matematicheskie Zametki, 2004, Volume 76, Issue 5, Pages 651–665
DOI: https://doi.org/10.4213/mzm136
(Mi mzm136)
 

This article is cited in 3 scientific papers (total in 3 papers)

Integrability of the Majorants of Fourier Series and Divergence of the Fourier Series of Functions with Restrictions on the Integral Modulus of Continuity

N. Yu. Antonov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (244 kB) Citations (3)
References:
Abstract: We construct an example of a function from the class $H_1^{\omega^*}$ , where $\omega^*(t)=\sqrt{\log\log(t^{-1})/\log(t^{-1})}$, $0<t\le t_0$, whose trigonometric Fourier series is divergent almost everywhere. We obtain sharp integrability conditions for the majorants of the partial sums of trigonometric Fourier series in terms of whether the functions in question belong to the classes $H_1^\omega$.
Received: 15.11.2003
English version:
Mathematical Notes, 2004, Volume 76, Issue 5, Pages 606–619
DOI: https://doi.org/10.1023/B:MATN.0000049660.29081.bc
Bibliographic databases:
UDC: 517.518
Language: Russian
Citation: N. Yu. Antonov, “Integrability of the Majorants of Fourier Series and Divergence of the Fourier Series of Functions with Restrictions on the Integral Modulus of Continuity”, Mat. Zametki, 76:5 (2004), 651–665; Math. Notes, 76:5 (2004), 606–619
Citation in format AMSBIB
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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