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(H-p - L-p)-Type inequalities for subsequences of Norlund means of Walsh-Fourier series
The University of Georgia, Georgia.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). UiT The Arctic University of Norway, Norway.ORCID iD: 0000-0002-5914-3247
UiT The Arctic University of Norway, Norway.
The University of Georgia, Georgia.
2023 (English)In: Journal of inequalities and applications, ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2023, no 1, article id 52Article in journal (Refereed) Published
Abstract [en]

We investigate the subsequence {t2n f} of Norlund means with respect to the Walsh system generated by nonincreasing and convex sequences. In particular, we prove that a large class of such summability methods are not bounded from the martingale Hardy spaces H-p to the space weak-Lp for 0 < p < 1/(1+ alpha), where 0 < alpha < 1. Moreover, some new related inequalities are derived. As applications, some well-known and new results are pointed out for well-known summability methods, especially for Norlund logarithmic means and Cesaro means.

Place, publisher, year, edition, pages
Springer, 2023. Vol. 2023, no 1, article id 52
Keywords [en]
Walsh system, Norlund means, Cesaro means, Norlund logarithmic means, Martingale Hardy space, Convergence, Divergence, Inequalities
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-94502DOI: 10.1186/s13660-023-02955-9ISI: 000964493300002Scopus ID: 2-s2.0-85152794489OAI: oai:DiVA.org:kau-94502DiVA, id: diva2:1754072
Available from: 2023-05-02 Created: 2023-05-02 Last updated: 2023-05-08Bibliographically approved

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Persson, Lars-Erik

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CiteExportLink to record
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Citation style
  • apa
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  • de-DE
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Output format
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