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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Weighted norm inequalities for Vilenkin-Fourier series


Author: Wo-Sang Young
Journal: Trans. Amer. Math. Soc. 340 (1993), 273-291
MSC: Primary 42C10; Secondary 42A20, 42A50, 43A50
DOI: https://doi.org/10.1090/S0002-9947-1993-1124174-3
MathSciNet review: 1124174
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Abstract: Let ${S_n}f$ be the $n$th partial sum of the Vilenkin-Fourier series of $f \in {L^1}$. For $1 < p < \infty$, we characterize all weight functions $w$ such that if $f \in {L^p}(w)$, ${S_n}f$ converges to $f$ in ${L^p}(w)$. We also determine all weight functions $w$ such that $\{ {S_n}\}$ is uniformly of weak type $(1,1)$ with respect to $w$.


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Article copyright: © Copyright 1993 American Mathematical Society