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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

An everywhere divergent Fourier-Walsh series of the class $ L({\rm log}\sp{+}{\rm log}\sp{+}L)\sp{1-\varepsilon }$


Author: K. H. Moon
Journal: Proc. Amer. Math. Soc. 50 (1975), 309-314
MSC: Primary 42A56
MathSciNet review: 0377406
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Abstract: Let $ \Phi $ be a function satisfying (a) $ \Phi (t) \geq 0$, convex and increasing; (b) $ \Phi ({t^{1/2}})$ is a concave function of $ t,0 \leq t < \infty $; and (c) $ \Phi (t) = 0(t\log \log t)$ as $ t \to \infty $. We construct a function in the class

$\displaystyle \Phi (L) = \{ f \in L(0,1):\int_0^1 {\Phi (\vert f(x)\vert)dx < \infty } \} $


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0377406-8
PII: S 0002-9939(1975)0377406-8
Keywords: Rademacher functions, Walsh functions, Fourier-Walsh series
Article copyright: © Copyright 1975 American Mathematical Society