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On the Convergence of Partial Sums with Respect to Vilenkin System on the Martingale Hardy Spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. University of Georgia, Tbilisi, Georgia.
2018 (English)In: Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), ISSN 1068-3623, Vol. 53, no 5, p. 294-306Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
Springer, 2018. Vol. 53, no 5, p. 294-306
Keywords [en]
Vilenkin system, partial sums, martingale Hardy space, modulus of continuity
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-71832DOI: 10.3103/S1068362318050072ISI: 000450525500007Scopus ID: 2-s2.0-85056725514OAI: oai:DiVA.org:ltu-71832DiVA, id: diva2:1267027
Note

Validerad;2018;Nivå 2;2018-11-30 (svasva)

Available from: 2018-11-30 Created: 2018-11-30 Last updated: 2019-01-10Bibliographically approved

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Tephnadze, George

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CiteExportLink to record
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Citation style
  • apa
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More styles
Language
  • de-DE
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  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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