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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Weighted norm inequalities for Vilenkin-Fourier series
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by Wo-Sang Young PDF
Trans. Amer. Math. Soc. 340 (1993), 273-291 Request permission

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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Additional Information
  • © Copyright 1993 American Mathematical Society
  • 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