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Proceedings of the American Mathematical Society

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Almost everywhere divergence of multiple Walsh-Fourier series


Author: David C. Harris
Journal: Proc. Amer. Math. Soc. 101 (1987), 637-643
MSC: Primary 42C10
DOI: https://doi.org/10.1090/S0002-9939-1987-0911024-3
MathSciNet review: 911024
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Abstract: C. Fefferman [1, 2, 3] has shown that the multiple Fourier series of an $ f \in {L^p},p < 2$, may diverge a.e. when summed over expanding spheres, but converges a.e. when summed over expanding polyhedral surfaces. We show this dichotomy does not prevail for multiple Walsh-Fourier series.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0911024-3
Keywords: Walsh functions, multiple Fourier series, a.e. divergence, multipliers
Article copyright: © Copyright 1987 American Mathematical Society