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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 3, Pages 193–200 (Mi izv342)  

This article is cited in 5 scientific papers (total in 5 papers)

$A$-integrable martingale sequences and Walsh series

V. A. Skvortsov

M. V. Lomonosov Moscow State University

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.

DOI: https://doi.org/10.4213/im342

Full text: PDF file (649 kB)
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English version:
Izvestiya: Mathematics, 2001, 65:3, 607–615

Bibliographic databases:

MSC: 40A05, 42C10, 43A75, 42C25, 60A05, 60G46
Received: 25.05.2000

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
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\crossref{https://doi.org/10.4213/im342}
\mathscinet{http://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-11844280523}


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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. Aliev R.A., “on Properties of Hilbert Transform of Finite Complex Measures”, Complex Anal. Oper. Theory, 10:1 (2016), 171–185  crossref  mathscinet  zmath  isi  scopus
    2. Aliev R.A., “on Laurent Coefficients of Cauchy Type Integrals of Finite Complex Measures”, Proc. Inst. Math. Mech., 42:2 (2016), 292–303  mathscinet  zmath  isi
    3. Aliev R.A., “Riesz'S Equality For the Hilbert Transform of the Finite Complex Measures”, Azerbaijan J. Math., 6:1 (2016), 126–135  mathscinet  zmath  isi  elib
    4. Aliev R.A., “Representability of Cauchy-type integrals of finite complex measures on the real axis in terms of their boundary values”, Complex Var. Elliptic Equ., 62:4 (2017), 536–553  crossref  mathscinet  zmath  isi  scopus
    5. Aliev R.A., Nebiyeva Kh. I., “The a-Integral and Restricted Ahlfors-Beurling Transform”, Integral Transform. Spec. Funct., 29:10 (2018), 820–830  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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