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A sharp boundedness result for restricted maximal operators of Vilenkin–Fourier series on martingale Hardy spaces
Institute of Mathematics and Computer Sciences, College of Nyíregyháza, Nyíregyháza, Hungary.
Institute of Mathematics and Computer Sciences, College of Nyíregyháza, Nyíregyháza, Hungary.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT the Arctic University of Norway, Narvik, Norway.
School of IT, Engineering and Mathematics, IV, University of Georgia, Tbilisi, Georgia.
2019 (Estonian)In: Georgian Mathematical Journal, ISSN 1072-947X, E-ISSN 1572-9176, Vol. 26, no 3Article in journal (Refereed) Published
Abstract [en]

The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space H p {H-{p}} to the Lebesgue space L p {L-{p}} for all 0 < p ≤ 1 {0<p\leq 1}. We also prove that the result is sharp in a particular sense. 

Place, publisher, year, edition, pages
Walter de Gruyter, 2019. Vol. 26, no 3
Keywords [en]
Vilenkin system, partial sums, maximal operator, Vilenkin–Fourier series, martingale Hardy space
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-71225DOI: 10.1515/gmj-2018-0045OAI: oai:DiVA.org:ltu-71225DiVA, id: diva2:1256374
Note

Validerad;2019;Nivå 2;2019-10-09 (johcin)

Available from: 2018-10-16 Created: 2018-10-16 Last updated: 2019-10-09Bibliographically approved

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Persson, Lars-Erik

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