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Mat. Zametki, 2009, Volume 85, Issue 4, Pages 502–515 (Mi mz6640)  

This article is cited in 3 scientific papers (total in 3 papers)

Almost Everywhere Divergent Subsequences of Fourier Sums of Functions from $\varphi(L)\cap H_1^\omega$

N. Yu. Antonov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: For a gap sequence of natural numbers $\{n_k\}^\infty_{k=1}$, for a nondecreasing function $\varphi\colon[0,+\infty)\to[0,+\infty)$ such that $\varphi(u)=o(u\ln\ln u)$ as $u\to\infty$, and a modulus of continuity satisfying the condition $(\ln k)^{-1}=O(\omega(n_k^{-1}))$, we present an example of a function $F\in\varphi(L)\cap H_1^\omega$ with an almost everywhere divergent subsequence $\{S_{n_k}(F,x)\}$ of the sequence of partial sums of the trigonometric Fourier series of the function $F$.

Keywords: Fourier sum, gap sequence, trigonometric Fourier series, modulus of continuity, Dirichlet kernel, Lebesgue measurability, Jensen's inequality

DOI: https://doi.org/10.4213/mzm6640

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English version:
Mathematical Notes, 2009, 85:4, 484–495

Bibliographic databases:

UDC: 517.518
Received: 15.01.2008
Revised: 04.07.2008

Citation: N. Yu. Antonov, “Almost Everywhere Divergent Subsequences of Fourier Sums of Functions from $\varphi(L)\cap H_1^\omega$”, Mat. Zametki, 85:4 (2009), 502–515; Math. Notes, 85:4 (2009), 484–495

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. 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
    2. 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
    3. Lie V., “The Pointwise Convergence of Fourier Series (II). Strong l(1)Case For the Lacunary Carleson Operator”, Adv. Math., 357 (2019), 106831  crossref  mathscinet  isi
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