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

 

A characterization of Lipschitz classes on finite dimensional groups


Author: Walter R. Bloom
Journal: Proc. Amer. Math. Soc. 59 (1976), 297-304
MSC: Primary 41A65; Secondary 43A70
MathSciNet review: 0417654
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Abstract: An analogue of a theorem of S. N. Bernstein is developed for certain metric locally compact abelian groups. This, together with a corresponding Jackson-type theorem, gives a characterisation in terms of their Fourier transforms of the Lipschitz functions defined on a compact abelian group with finite topological dimension.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0417654-2
PII: S 0002-9939(1976)0417654-2
Article copyright: © Copyright 1976 American Mathematical Society