RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 2000, Volume 191, Number 1, Pages 103–126 (Mi msb449)  

This article is cited in 24 scientific papers (total in 25 papers)

On everywhere divergence of trigonometric Fourier series

S. V. Konyagin

M. V. Lomonosov Moscow State University

Abstract: The following theorem is established.
Theorem. {\it Let a function $\varphi\colon[0,+\infty)\to[0,+\infty)$ and a sequence $\{\psi(m)\}$ satisfy the following condition: the function $\varphi(u)/u$ is non-decreasing on $(0,+\infty)$, $\psi(m)\geqslant 1$ $(m=1,2,…)$ and $\varphi(m)\psi(m)=o(m\sqrt{\ln m}/\sqrt{\ln\ln m} )$ as $m\to\infty$. Then there is a function $f\in L[-\pi,\pi]$ such that
$$ \int _{-\pi}^\pi\varphi(|f(x)|) dx<\infty $$
and $\limsup_{m\to\infty}S_m(f,x)/\psi(m)=\infty$ for all $x\in[-\pi,\pi]$ here $S_m(f)$ is the $m$-th partial sum of the trigonometric Fourier series of $f$}.

DOI: https://doi.org/10.4213/sm449

Full text: PDF file (339 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2000, 191:1, 97–120

Bibliographic databases:

Document Type: Article
UDC: 517.518.45
MSC: 42a20
Received: 11.06.1999

Citation: S. V. Konyagin, “On everywhere divergence of trigonometric Fourier series”, Mat. Sb., 191:1 (2000), 103–126; Sb. Math., 191:1 (2000), 97–120

Citation in format AMSBIB
\Bibitem{Kon00}
\by S.~V.~Konyagin
\paper On everywhere divergence of trigonometric Fourier series
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 1
\pages 103--126
\mathnet{http://mi.mathnet.ru/msb449}
\crossref{https://doi.org/10.4213/sm449}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1753494}
\zmath{https://zbmath.org/?q=an:0967.42004}
\transl
\jour Sb. Math.
\yr 2000
\vol 191
\issue 1
\pages 97--120
\crossref{https://doi.org/10.1070/sm2000v191n01ABEH000449}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000087494000004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0034341425}


Linking options:
  • http://mi.mathnet.ru/eng/msb449
  • https://doi.org/10.4213/sm449
  • http://mi.mathnet.ru/eng/msb/v191/i1/p103

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Arias-De-Reyna J., “Pointwise convergence of Fourier series”, J. London Math. Soc. (2), 65 (2002), 139–153  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    2. N. Yu. Antonov, “Almost everywhere convergence over cubes of multiple trigonometric Fourier series”, Izv. Math., 68:2 (2004), 223–241  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. 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”, Math. Notes, 76:5 (2004), 606–619  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Lacey M.T., “Carleson's theorem: proof, complements, variations”, Publ. Mat., 48:2 (2004), 251–307  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. N. Yu. Antonov, “Growth rate of sequences of multiple rectangular Fourier sums”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S9–S29  mathnet  mathscinet  zmath  elib
    6. S. V. Konyagin, “Divergence everywhere of subsequences of partial sums of trigonometric Fourier series”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S167–S175  mathnet  mathscinet  zmath  elib
    7. G. A. Karagulian, “Everywhere Divergent $\Phi$-Means of Fourier Series”, Math. Notes, 80:1 (2006), 47–56  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. N. Yu. Antonov, “On the almost everywhere convergence of sequences of multiple rectangular Fourier sums”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S1–S18  mathnet  crossref  isi  elib
    9. 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
    10. N. Yu. Antonov, “On the growth rate of arbitrary sequences of double rectangular Fourier sums”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S14–S20  mathnet  crossref  isi  elib
    11. Bochkarev S.V., “On a Problem of Hardy for Walsh-Fourier Series”, Doklady Mathematics, 81:3 (2010), 390–391  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    12. I. V. Polyakov, “Example of a Divergent Fourier Series in the Vilenkin System”, Math. Notes, 89:5 (2011), 734–740  mathnet  crossref  crossref  mathscinet  isi
    13. I. V. Polyakov, “Examples of divergent Fourier series for a wide class of rearranged Walsh–Paley system”, Moscow University Mathematics Bulletin, 68:1 (2013), 1–6  mathnet  crossref
    14. G. Gát, U. Goginava, G. Karagulyan, “On everywhere divergence of the strong Φ-means of Walsh–Fourier series”, Journal of Mathematical Analysis and Applications, 2014  crossref  mathscinet  scopus  scopus  scopus
    15. I. V. Polyakov, “Estimates of the Dirichlet Kernel and Divergent Fourier Series in the Walsh–Kaczmarz System”, Math. Notes, 95:2 (2014), 234–246  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    16. R. M. Trigub, “Summability of trigonometric Fourier series at $d$-points and a generalization of the Abel–Poisson method”, Izv. Math., 79:4 (2015), 838–858  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. N. Yu. Antonov, “On almost everywhere convergence for lacunary sequences of multiple rectangular Fourier sums”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 43–59  mathnet  crossref  mathscinet  elib
    18. R. M. Trigub, “Almost Everywhere Summability of Fourier Series with Indication of the Set of Convergence”, Math. Notes, 100:1 (2016), 139–153  mathnet  crossref  crossref  mathscinet  isi  elib
    19. Lie V., “Pointwise Convergence of Fourier Series (i). on a Conjecture of Konyagin”, J. Eur. Math. Soc., 19:6 (2017), 1655–1728  crossref  mathscinet  zmath  isi  scopus
    20. Nikolai Yu. Antonov, “On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series”, Ural Math. J., 3:2 (2017), 14–21  mathnet  crossref
    21. Weisz F., “Convergence and Summability of Fourier Transforms and Hardy Spaces”, Convergence and Summability of Fourier Transforms and Hardy Spaces, Applied and Numerical Harmonic Analysis, Birkhauser Boston, 2017, 1–435  crossref  mathscinet  isi
    22. Mastylo M., Rodriguez-Piazza L., “Convergence Almost Everywhere of Multiple Fourier Series Over Cubes”, Trans. Am. Math. Soc., 370:3 (2018), 1629–1659  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    23. S. V. Bochkarev, “An abstract Kolmogorov theorem, and an application to metric spaces and topological groups”, Sb. Math., 209:11 (2018), 1575–1602  mathnet  crossref  crossref  adsnasa  isi  elib
    24. B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, K. S. Ryutin, I. D. Shkredov, “Sergei Vladimirovich Konyagin turns 60”, Proc. Steklov Inst. Math., 303 (2018), 1–9  mathnet  crossref  crossref  isi  elib
    25. Edmunds D., Gogatishvili A., Kopaliani T., “Construction of Function Spaces Close to l With Associate Space Close to l-1”, J. Fourier Anal. Appl., 24:6 (2018), 1539–1553  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:662
    Full text:209
    References:54
    First page:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019