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

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2005, Volume 11, Number 2, Pages 112–119 (Mi timm193)

This article is cited in 8 scientific papers (total in 9 papers)

Divergence everywhere of subsequences of partial sums of trigonometric Fourier series

S. V. Konyagin

Full-text PDF (244 kB) Citations (9)

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Abstract: It is proved that for any increasing sequence of natural numbers

{m_{j}}

$\{m_j\}$ and any nondecreasing function

φ : [0, + \infty) \to [0, + \infty)

$\varphi\colon[0,+\infty)\to[0,+\infty)$ satisfying the condition

φ (u) = o (u \ln \ln)

$\varphi(u)=o(u\ln\ln)$ (

u \to \infty

$u\to\infty$ ) there is a function

f \in L [0, 2 π]

$f\in L[0,2\pi]$ such that

\int_{0}^{2 π} φ (| f (x) |) d x < \infty,

$\int_0^{2\pi}\varphi(|f(x)|)\,dx<\infty,$
and the Fourier partial sums

S_{m_{j}} (f)

$S_{m_j}(f)$ diverge unboundedly everywhere.

Received: 20.09.2004

Bibliographic databases:

Document Type: Article

UDC: 517.518.45

Language: Russian

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://mathscinet.ams.org/mathscinet-getitem?mr=2200228}

\zmath{https://zbmath.org/?q=an:1135.42005}

\elib{https://elibrary.ru/item.asp?id=12040707}

\transl

\jour Proc. Steklov Inst. Math. (Suppl.)

\yr 2005

\issue , suppl. 2

\pages S167--S175

Linking options:

https://www.mathnet.ru/eng/timm193

https://www.mathnet.ru/eng/timm/v11/i2/p112

This publication is cited in the following 9 articles:

G. G. Oniani, “On the Divergence Sets of Fourier Series in Systems of Characters of Compact Abelian Groups”, Math. Notes, 112:1 (2022), 100–108
Goginava U., Oniani G., “On the Divergence of Subsequences of Partial Walsh-Fourier Sums”, J. Math. Anal. Appl., 497:2 (2021), 124900
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
Lie V., “Pointwise Convergence of Fourier Series (i). on a Conjecture of Konyagin”, J. Eur. Math. Soc., 19:6 (2017), 1655–1728
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
Do Y.Q., Lacey M.T., “On the convergence of lacunary Walsh-Fourier series”, Bull London Math Soc, 44:2 (2012), 241–254
Lie V., “On the Pointwise Convergence of the Sequence of Partial Fourier Sums Along Lacunary Subsequences”, J. Funct. Anal., 263:11 (2012), 3391–3411
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
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

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Trudy Instituta Matematiki i Mekhaniki UrO RAN

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