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Izvestiya: Mathematics, 2001, Volume 65, Issue 3, Pages 607–615
DOI: https://doi.org/10.1070/IM2001v065n03ABEH000342 (Mi im342) 		 
This article is cited in 9 scientific papers (total in 9 papers)

$A$-integrable martingale sequences and Walsh series

V. A. Skvortsov

M. V. Lomonosov Moscow State University
English version PDF (143 kB) Citations (9)
References:
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DOI: https://doi.org/10.1070/IM2001v065n03ABEH000342
Abstract: A sufficient condition for a Walsh series converging to an $A$-integrable function $f$ to be the $A$-Fourier's series of $f$ is stated in terms of uniform $A$-integrability of a martingale subsequence of partial sums of the Walsh series. Moreover, the existence is proved of a Walsh series that converges almost everywhere to an $A$-integrable function and is not the $A$-Fourier series of its sum.
Received: 25.05.2000
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2001, Volume 65, Issue 3, Pages 193–200
DOI: https://doi.org/10.4213/im342
Bibliographic databases:
MSC: 40A05, 42C10, 43A75, 42C25, 60A05, 60G46
Language: English
Original paper language: Russian
Citation: V. A. Skvortsov, “$A$-integrable martingale sequences and Walsh series”, Izv. RAN. Ser. Mat., 65:3 (2001), 193–200; Izv. Math., 65:3 (2001), 607–615
Citation in format AMSBIB
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\by V.~A.~Skvortsov
\paper $A$-integrable martingale sequences and Walsh series
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 3
\pages 193--200
\mathnet{http://mi.mathnet.ru/im342}
\crossref{https://doi.org/10.4213/im342}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1853372}
\zmath{https://zbmath.org/?q=an:0992.42014}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 3
\pages 607--615
\crossref{https://doi.org/10.1070/IM2001v065n03ABEH000342}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-11844280523}
Linking options:
  • https://www.mathnet.ru/eng/im342
  • https://doi.org/10.1070/IM2001v065n03ABEH000342
  • https://www.mathnet.ru/eng/im/v65/i3/p193
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:561
    Russian version PDF:218
    English version PDF:12
    References:72
    First page:3
     
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