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Trudy Inst. Mat. i Mekh. UrO RAN, 2005, Volume 11, Number 2, Pages 112–119 (Mi timm193)  

This article is cited in 6 scientific papers (total in 7 papers)

Divergence everywhere of subsequences of partial sums of trigonometric Fourier series

S. V. Konyagin


Abstract: It is proved that for any increasing sequence of natural numbers $\{m_j\}$ and any nondecreasing function $\varphi\colon[0,+\infty)\to[0,+\infty)$ satisfying the condition $\varphi(u)=o(u\ln\ln)$ ($u\to\infty$) there is a function $f\in L[0,2\pi]$ such that
$$ \int_0^{2\pi}\varphi(|f(x)|) dx<\infty, $$
and the Fourier partial sums $S_{m_j}(f)$ diverge unboundedly everywhere.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2005, suppl. 2, S167–S175

Bibliographic databases:

Document Type: Article
UDC: 517.518.45
Received: 20.09.2004

Citation: S. V. Konyagin, “Divergence everywhere of subsequences of partial sums of trigonometric Fourier series”, Function theory, Trudy Inst. Mat. i Mekh. UrO RAN, 11, no. 2, 2005, 112–119; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S167–S175

Citation in format AMSBIB
\Bibitem{Kon05}
\by S.~V.~Konyagin
\paper Divergence everywhere of subsequences of partial sums of trigonometric Fourier series
\inbook Function theory
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2005
\vol 11
\issue 2
\pages 112--119
\mathnet{http://mi.mathnet.ru/timm193}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200228}
\zmath{https://zbmath.org/?q=an:1135.42005}
\elib{http://elibrary.ru/item.asp?id=12040707}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2005
\issue , suppl. 2
\pages S167--S175


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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. Do Y.Q., Lacey M.T., “On the convergence of lacunary Walsh-Fourier series”, Bull London Math Soc, 44:2 (2012), 241–254  crossref  mathscinet  zmath  isi  elib  scopus
    3. Lie V., “On the Pointwise Convergence of the Sequence of Partial Fourier Sums Along Lacunary Subsequences”, J. Funct. Anal., 263:11 (2012), 3391–3411  crossref  mathscinet  zmath  isi  elib  scopus
    4. Tsukareva Z.N., “Slabaya obobschennaya lokalizatsiya dlya kratnykh ryadov fure s lakunarnoi posledovatelnostyu chastichnykh summ v klassakh orlicha”, Vestnik moskovskogo gosudarstvennogo oblastnogo universiteta. seriya: fizika-matematika, 2012, no. 1, 18–23  elib
    5. 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  isi  elib
    6. 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
    7. 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
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