Some weak type inequalities and almost everywhere convergence of Vilenkin–Nörlund means

We prove and discuss some new weak type ( 1 , 1 ) inequalities of maximal operators of Vilenkin–Nörlund means generated by monotone coefficients. Moreover, we use these results to prove a.e. convergence of such Vilenkin–Nörlund means. As applications, both some well-known and new inequalities are po...

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Published inJournal of inequalities and applications Vol. 2023; no. 1; pp. 66 - 17
Main Authors Baramidze, Davit, Nadirashvili, Nato, Persson, Lars-Erik, Tephnadze, George
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 04.05.2023
Springer Nature B.V
Springer
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Convergence
Inequalities
Inequality
Martingale Hardy space
Matematik
Mathematical functions
Mathematics
Mathematics and Statistics
Maximal operator
Norlund means
Number systems
Nörlund means
Vilenkin group
Vilenkin system
Vilenkin-Fourier series
W e a k − L p $Weak-L^{p}$ spaces
Weak - L-p spaces
Weak type inequality
42C10
Nörlund means
Vilenkin group
Weak type inequality
Vilenkin–Fourier series
42B30
Maximal operator
spaces
Vilenkin system
26015
Martingale Hardy space
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Summary:We prove and discuss some new weak type ( 1 , 1 ) inequalities of maximal operators of Vilenkin–Nörlund means generated by monotone coefficients. Moreover, we use these results to prove a.e. convergence of such Vilenkin–Nörlund means. As applications, both some well-known and new inequalities are pointed out.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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Journal of Inequalities and Applications
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-023-02970-w