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Russian Mathematical Surveys, 2004, Volume 59, Issue 1, Pages 103–124
DOI: https://doi.org/10.1070/RM2004v059n01ABEH000703
(Mi rm703)
 

This article is cited in 17 scientific papers (total in 18 papers)

Everywhere divergent Fourier series with respect to the Walsh system and with respect to multiplicative systems

S. V. Bochkarev

Steklov Mathematical Institute, Russian Academy of Sciences
References:
Abstract: In this paper a new construction of everywhere divergent Fourier–Walsh series is presented. This construction enables one to halve the gap in the Lebesgue–Orlicz classes between the Schipp–Moon lower bound established by using Kolmogorov's construction and the Sjölin upper bound obtained by using Carleson's method. Fourier series which are everywhere divergent after a rearrangement are constructed with respect to the Walsh system (and to more general systems of characters) with the best lower bound for the Weyl factor. Some results related to an upper bound of the majorant for partial sums of series with respect to rearranged multiplicative systems are established. The results thus obtained show certain merits of harmonic analysis on the dyadic group in clarifying and overcoming fundamental difficulties in the solution of the main problems of Fourier analysis.
Received: 20.11.2003
Russian version:
Uspekhi Matematicheskikh Nauk, 2004, Volume 59, Issue 1(355), Pages 103–124
DOI: https://doi.org/10.4213/rm703
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: Primary 42C10; Secondary 42A20, 42C20, 42C15
Language: English
Original paper language: Russian
Citation: S. V. Bochkarev, “Everywhere divergent Fourier series with respect to the Walsh system and with respect to multiplicative systems”, Uspekhi Mat. Nauk, 59:1(355) (2004), 103–124; Russian Math. Surveys, 59:1 (2004), 103–124
Citation in format AMSBIB
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\pages 103--124
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  • https://doi.org/10.1070/RM2004v059n01ABEH000703
  • https://www.mathnet.ru/eng/rm/v59/i1/p103
  • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Успехи математических наук Russian Mathematical Surveys
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    Abstract page:781
    Russian version PDF:335
    English version PDF:22
    References:84
    First page:3
     
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