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A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients
Department of mathematics, University of Sarajevo.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Number of Authors: 32016 (English)In: Studia scientiarum mathematicarum Hungarica (Print), ISSN 0081-6906, E-ISSN 1588-2896, Vol. 53, no 4, p. 545-556Article in journal (Refereed) Published
Abstract [en]

In [14] we investigated some Vilenkin—Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H1/(1+α) to the space weak-L1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H1/(1+α), which satisfies the conditions considered in [14], and so that the maximal operators of these Vilenkin—Nörlund means with non-increasing coefficients are not bounded from the Hardy space H1/(1+α) to the space L1/(1+α). In particular, this shows that the conditions under which the result in [14] is proved are in a sense sharp. Moreover, as further applications, some well-known and new results are pointed out.

Place, publisher, year, edition, pages
2016. Vol. 53, no 4, p. 545-556
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-8860DOI: 10.1556/012.2016.53.4.1342ISI: 000388813600007Scopus ID: 2-s2.0-84996837296Local ID: 76930bce-6769-4330-b68b-b1c2a6227492OAI: oai:DiVA.org:ltu-8860DiVA, id: diva2:981798
Note

Validerad; 2016; Nivå 2; 2016-12-05 (inah)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Persson, Lars-ErikTephnadze, George

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