RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
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. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


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

This article is cited in 2 scientific papers (total in 2 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

Full text: PDF file (548 kB)
References: PDF file   HTML file

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
\Bibitem{Ant09}
\by N.~Yu.~Antonov
\paper Almost Everywhere Divergent Subsequences of Fourier Sums of Functions from $\varphi(L)\cap H_1^\omega$
\jour Mat. Zametki
\yr 2009
\vol 85
\issue 4
\pages 502--515
\mathnet{http://mi.mathnet.ru/mz6640}
\crossref{https://doi.org/10.4213/mzm6640}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2549413}
\zmath{https://zbmath.org/?q=an:05628178}
\elib{http://elibrary.ru/item.asp?id=15305483}
\transl
\jour Math. Notes
\yr 2009
\vol 85
\issue 4
\pages 484--495
\crossref{https://doi.org/10.1134/S0001434609030201}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000266561100020}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70249106439}


Linking options:
  • http://mi.mathnet.ru/eng/mz6640
  • https://doi.org/10.4213/mzm6640
  • http://mi.mathnet.ru/eng/mz/v85/i4/p502

    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. 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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:364
    Full text:74
    References:55
    First page:15

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