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On the Convergence of Partial Sums with Respect to Vilenkin System on the Martingale Hardy Spaces

  • Real and Complex Analysis
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Abstract

In this paper, we derive characterizations of boundedness of subsequences of partial sums with respect to Vilenkin system on the martingale Hardy spaces Hp when 0 < p < 1. Moreover, we find necessary and sufficient conditions for the modulus of continuity of martingales f ∈ Hp, which provide convergence of subsequences of partial sums on the martingale Hardy spaces Hp. It is also proved that these results are the best possible in a special sense. As applications, some known and new results are pointed out.

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Authors and Affiliations

  1. University of Georgia, Tbilisi, Georgia

    G. Tephnadze

  2. Luleå University of Technology, Luleå, Sweden

    G. Tephnadze

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  1. G. Tephnadze
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Correspondence to G. Tephnadze.

Additional information

Original Russian Text © G. Tephnadze, 2018, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2018, No. 5, pp. 77–94.

The research was supported by Shota Rustaveli National Science Foundation grants no. DO/24/5-100/14 and YS15-2.1.1-47, by a Swedish Institute scholarship no. 10374–2015 and by target scientific research programs grant for the students of faculty of Exact and Natural Sciences.

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Tephnadze, G. On the Convergence of Partial Sums with Respect to Vilenkin System on the Martingale Hardy Spaces. J. Contemp. Mathemat. Anal. 53, 294–306 (2018). https://doi.org/10.3103/S1068362318050072

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  • DOI: https://doi.org/10.3103/S1068362318050072

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