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Mat. Zametki, 2006, Volume 80, Issue 1, Pages 50–59 (Mi mz2779)  

This article is cited in 9 scientific papers (total in 9 papers)

Everywhere Divergent $\Phi$-Means of Fourier Series

G. A. Karagulian

Institute of Mathematics, National Academy of Sciences of Armenia

Abstract: For a function $f\in L^1({\mathbb T})$, we investigate the sequence $(C,1)$ of mean values $\Phi(|S_k(x,f)-f(x)|)$, where $\Phi (t)\colon [0,+\infty)\to [0,+\nobreak \infty)$, $\Phi (0)=\nobreak 0$, is a continuous increasing function. We prove that if $\Phi $ increases faster than exponentially, then these means can diverge everywhere. Divergence almost everywhere of such means was established earlier.

Keywords: Fourier series, means of Fourier series, the space $L^1({\mathbf T})$

DOI: https://doi.org/10.4213/mzm2779

Full text: PDF file (449 kB)
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English version:
Mathematical Notes, 2006, 80:1, 47–56

Bibliographic databases:

UDC: 517
Received: 28.04.2005
Revised: 07.10.2005

Citation: G. A. Karagulian, “Everywhere Divergent $\Phi$-Means of Fourier Series”, Mat. Zametki, 80:1 (2006), 50–59; Math. Notes, 80:1 (2006), 47–56

Citation in format AMSBIB
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\by G.~A.~Karagulian
\paper Everywhere Divergent
$\Phi$-Means of Fourier Series
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\yr 2006
\vol 80
\issue 1
\pages 50--59
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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. Gat G. Goginava U. Karagulyan G., “Almost Everywhere Strong Summability of Marcinkiewicz Means of Double Walsh-Fourier Series”, Anal. Math., 40:4 (2014), 243–266  crossref  mathscinet  zmath  isi  scopus
    2. Goginava U. Gogoladze L. Karagulyan G., “Bmo-Estimation and Almost Everywhere Exponential Summability of Quadratic Partial Sums of Double Fourier Series”, Constr. Approx., 40:1 (2014), 105–120  crossref  mathscinet  zmath  isi  scopus
    3. Gat G. Goginava U., “Almost Everywhere Strong Summability of Double Walsh-Fourier Series”, J. Contemp. Math. Anal.-Armen. Aca., 50:1 (2015), 1–13  crossref  mathscinet  zmath  isi  scopus
    4. Gat G., Goginava U., Karagulyan G., “On Everywhere Divergence of the Strong Phi-Means of Walsh-Fourier Series”, J. Math. Anal. Appl., 421:1 (2015), 206–214  crossref  mathscinet  zmath  isi  scopus
    5. Wilson B., “on Almost Everywhere Convergence of Strong Arithmetic Means of Fourier Series”, Trans. Am. Math. Soc., 367:2 (2015), 1467–1500  crossref  mathscinet  zmath  isi
    6. Goginava U., “Almost Everywhere Strong Summability of Cubic Partial Sums of D-Dimensional Walsh-Fourier Series”, Math. Inequal. Appl., 20:4 (2017), 1051–1066  crossref  mathscinet  zmath  isi  scopus
    7. Goginava U., “Almost Everywhere Strong Summability of Fej,R Means of Rectangular Partial Sums of Two-Dimensional Walsh-Fourier Series”, J. Contemp. Math. Anal.-Armen. Aca., 53:2 (2018), 100–112  crossref  mathscinet  isi
    8. U. Goginava, G. Karagulian, “On Exponential Summability of Rectangular Partial Sums of Double Trigonometric Fourier Series”, Math. Notes, 104:5 (2018), 655–665  mathnet  crossref  crossref  isi  elib
    9. Goginava U., “Almost Everywhere Convergence of Strong Norlund Logarithmic Means of Walsh-Fourier Series”, J. Contemp. Math. Anal.-Armen. Aca., 53:5 (2018), 281–287  crossref  mathscinet  zmath  isi  scopus
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