Almost everywhere divergence of multiple Walsh-Fourier series-Reference-Cited by-同舟云学术

Almost everywhere divergence of multiple Walsh-Fourier series

Published:1987 Issue:4 Volume:101 Page:637-643
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Harris David C.

Abstract

C. Fefferman [1, 2, 3] has shown that the multiple Fourier series of an f ∈ L p , p > 2 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1987-101-04/S0002-9939-1987-0911024-3/S0002-9939-1987-0911024-3.pdf

Reference8 articles.

1. Inequalities for strongly singular convolution operators;Fefferman, Charles;Acta Math.,1970

2. The multiplier problem for the ball;Fefferman, Charles;Ann. of Math. (2),1971

3. On the convergence of multiple Fourier series;Fefferman, Charles;Bull. Amer. Math. Soc.,1971

4. On the Walsh functions;Fine, N. J.;Trans. Amer. Math. Soc.,1949

5. Interscience Tracts in Pure and Applied Mathematics, No. 12;Rudin, Walter,1962

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