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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
DOI: https://doi.org/10.1090/S0002-9939-1976-0417654-2
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.


References [Enhancements On Off] (What's this?)

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  • [5] P. L. Walker, Lipschitz classes on finite dimensional groups, Proc. Cambridge Philos. Soc. 66 (1969), 31-38. MR 39 #1912. MR 0240565 (39:1912)
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DOI: https://doi.org/10.1090/S0002-9939-1976-0417654-2
Article copyright: © Copyright 1976 American Mathematical Society

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