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Mat. Zametki, 2004, Volume 76, Issue 5, Pages 651–665 (Mi mz136)  

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

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 $H_1^\omega$.

DOI: https://doi.org/10.4213/mzm136

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English version:
Mathematical Notes, 2004, 76:5, 606–619

Bibliographic databases:

UDC: 517.518
Received: 15.11.2003

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. Yu. Antonov, “Almost Everywhere Divergent Subsequences of Fourier Sums of Functions from $\varphi(L)\cap H_1^\omega$”, Math. Notes, 85:4 (2009), 484–495  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. S. V. Konyagin, “Almost everywhere divergence of lacunary subsequences of partial sums of Fourier series”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S99–S106  mathnet  crossref  isi  elib
    3. N. Yu. Antonov, “Estimates for the growth order of sequences of multiple rectangular Fourier sums of integrable functions”, J. Math. Sci., 209:1 (2015), 1–11  mathnet  crossref  mathscinet
  • Математические заметки Mathematical Notes
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