Norm summability of Nörlund logarithmic means on unbounded Vilenkin groups

The (Nörlund) logarithmic means of the Fourier series is: . In general, the Fejér ( C ,1) means have better properties than the logarithmic ones. We compare them and show that in the case of some unbounded Vilenkin systems the situation changes.

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Bibliographic Details
Published inAnalysis in theory & applications Vol. 24; no. 1; pp. 1 - 17
Main Authors Blahota, István, Gát, György
Format Journal Article
LanguageEnglish
Published Heidelberg Editorial Board of Analysis in Theory and Applications 01.03.2008
Subjects
Analysis
Approximations and Expansions
Mathematics
Mathematics and Statistics
unbounded Vilenkin group
42C10
Fejér means
norm convergence
logarithmic means
Online AccessGet full text
ISSN1672-4070
1573-8175
DOI10.1007/s10496-008-0001-z

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Summary:The (Nörlund) logarithmic means of the Fourier series is: . In general, the Fejér ( C ,1) means have better properties than the logarithmic ones. We compare them and show that in the case of some unbounded Vilenkin systems the situation changes.
ISSN:1672-4070
1573-8175
DOI:10.1007/s10496-008-0001-z