Almost everywhere divergence of multiple Walsh-Fourier series

Harris, David C.

doi:10.1090/S0002-9939-1987-0911024-3

Almost everywhere divergence of multiple Walsh-Fourier series
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Proc. Amer. Math. Soc. 101 (1987), 637-643 Request permission

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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