Email this article On the Convergence of Partial Sums with Respect to Vilenkin System on the Martingale Hardy Spaces
- Authors: Tephnadze G.1,2
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Affiliations:
- University of Georgia
- Luleå University of Technology
- Issue: Vol 53, No 5 (2018)
- Pages: 294-306
- Section: Real and Complex Analysis
- URL: https://journal-vniispk.ru/1068-3623/article/view/228240
- DOI: https://doi.org/10.3103/S1068362318050072
- ID: 228240
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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.
About the authors
G. Tephnadze
University of Georgia; Luleå University of Technology
Author for correspondence.
Email: giorgitephnadze@gmail.com
Georgia, Tbilisi; Luleå
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