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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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On rearrangements of Vilenkin-Fourier series which preserve almost everywhere convergence
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by J. A. Gosselin and W. S. Young PDF
Trans. Amer. Math. Soc. 209 (1975), 157-174 Request permission

Abstract:

It is known that the partial sums of Vilenkin-Fourier series of ${L^q}$ functions $(q > 1)$ converge a.e. In this paper we establish the ${L^2}$ result for a class of rearrangements of the Vilenkin-Fourier series, and the ${L^q}$ result $(1 < q < 2)$ for a subclass of rearrangements. In the case of the Walsh-Fourier series, these classes include the Kaczmarz rearrangement studied by L. A. Balashov. The ${L^2}$ result for the Kaczmarz rearrangement was first proved by K. H. Moon. The techniques of proof involve a modification of the Carleson-Hunt method and estimates on maximal functions of the Hardy-Littlewood type that arise from these rearrangements.
References
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 209 (1975), 157-174
  • MSC: Primary 43A50; Secondary 42A56
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0399756-6
  • MathSciNet review: 0399756