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Generalized Lipschitz Spaces on Vilenkin Groups

Bloom, W.R. and Fournier, J.J.F. (1987) Generalized Lipschitz Spaces on Vilenkin Groups. Mathematische Nachrichten, 132 (1). pp. 67-80.

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It is shown that, for certain choices of the defining indices, the generalized Lipschitz spaces on Vilenkin groups are included in certain Figà-Talamanca spaces Ap, and that the Fourier series of functions in the latter spaces converge uniformly. This result includes an extension of the classical Dini test, and endpoint versions of Bernstein's theorem on absolute convergence of Fourier series.

Item Type: Journal Article
Murdoch Affiliation(s): School of Mathematical and Physical Sciences
Publisher: Wiley
Copyright: © 1987 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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