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\(L^1\)-Convergence of Double Vilenkin Series

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Abstract

We give necessary and sufficient conditions for \(L^1\) convergence of double Vilenkin series whose coefficients form a double null sequence of bounded variation. Also we study the existence of the special form of Riemann improper integral for sum of this series.

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References

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Funding

The work of the second author was supported by the Program of development of Regional Scientific and Educational Mathematical Center “Mathematics of Future Technologies” (project no. 075-02-2023-949)

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Saratov State University, Astrakhanskaya Str. 83, Saratov, 410012, Russia

    N. Yu. Agafonova & S. S. Volosivets

Authors
  1. N. Yu. Agafonova
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  2. S. S. Volosivets
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Correspondence to N. Yu. Agafonova or S. S. Volosivets.

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Agafonova, N.Y., Volosivets, S.S. \(L^1\)-Convergence of Double Vilenkin Series. P-Adic Num Ultrametr Anal Appl 15, 94–103 (2023). https://doi.org/10.1134/S2070046623020024

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  • DOI: https://doi.org/10.1134/S2070046623020024

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