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Sbornik: Mathematics, 2018, Volume 209, Issue 1, Pages 35–55
DOI: https://doi.org/10.1070/SM8806
(Mi sm8806)
 

This article is cited in 15 scientific papers (total in 15 papers)

The structure of universal functions for $L^p$-spaces, $p\in(0,1)$

M. G. Grigoryana, A. A. Sargsyanb

a Yerevan State University, Armenia
b Russian-Armenian (Slavonic) State University, Yerevan, Armenia
References:
Abstract: The paper sheds light on the structure of functions which are universal for $L^p$-spaces, $p\in(0,1)$, with respect to the signs of Fourier-Walsh coefficients. It is shown that there exists a measurable set $E\subset [0,1]$, whose measure is arbitrarily close to $1$, such that by an appropriate change of values of any function $f\in L^1[0,1]$ outside $E$ a function $\widetilde f\in L^1[0,1]$ can be obtained that is universal for each $L^p[0,1]$-space, $p\in(0,1)$, with respect to the signs of Fourier-Walsh coefficients.
Bibliography: 28 titles.
Keywords: universal function, Fourier coefficients, Walsh system, convergence in a metric.
Received: 27.08.2016 and 27.01.2017
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 1, Pages 37–57
DOI: https://doi.org/10.4213/sm8806
Bibliographic databases:
Document Type: Article
UDC: 517.51
MSC: 42C10, 43A15
Language: English
Original paper language: Russian
Citation: M. G. Grigoryan, A. A. Sargsyan, “The structure of universal functions for $L^p$-spaces, $p\in(0,1)$”, Mat. Sb., 209:1 (2018), 37–57; Sb. Math., 209:1 (2018), 35–55
Citation in format AMSBIB
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\paper The structure of universal functions for $L^p$-spaces, $p\in(0,1)$
\jour Mat. Sb.
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\vol 209
\issue 1
\pages 37--57
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\crossref{https://doi.org/10.4213/sm8806}
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\jour Sb. Math.
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\vol 209
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\pages 35--55
\crossref{https://doi.org/10.1070/SM8806}
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Linking options:
  • https://www.mathnet.ru/eng/sm8806
  • https://doi.org/10.1070/SM8806
  • https://www.mathnet.ru/eng/sm/v209/i1/p37
  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
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    Abstract page:626
    Russian version PDF:56
    English version PDF:12
    References:60
    First page:32
     
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