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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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DOI: https://doi.org/10.1090/S0002-9947-1993-1124174-3
Article copyright: © Copyright 1993 American Mathematical Society

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