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A characterisation of Lipschitz classes on 0-dimensional groups


Author: Walter R. Bloom
Journal: Proc. Amer. Math. Soc. 53 (1975), 149-154
MSC: Primary 43A15; Secondary 41A65
DOI: https://doi.org/10.1090/S0002-9939-1975-0383000-5
MathSciNet review: 0383000
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Abstract: This paper is concerned with characterising, in terms of certain properties of their Fourier transforms, the Lipschitz functions of order $ \alpha (0 < \alpha < 1)$ defined on a locally compact metric 0-dimensional Abelian group.


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

  • [1] Walter R. Bloom, Bernstein’s inequality for locally compact abelian groups, J. Austral. Math. Soc. 17 (1974), 88–101. Collection of articles dedicated to the memory of Hanna Neumann, V. MR 0348395
  • [2] Walter R. Bloom, Jackson’s theorem for locally compact abelian groups, Bull. Austral. Math. Soc. 10 (1974), 59–66. MR 0336227, https://doi.org/10.1017/S0004972700040624
  • [3] Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
  • [4] P. L. Walker, Lipschitz classes on 0-dimensional groups, Proc. Cambridge Philos. Soc. 63 (1967), 923–928. MR 0216246
  • [5] A. Zygmund, Trigonometric series: Vols. I, II, Second edition, reprinted with corrections and some additions, Cambridge University Press, London-New York, 1968. MR 0236587

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DOI: https://doi.org/10.1090/S0002-9939-1975-0383000-5
Article copyright: © Copyright 1975 American Mathematical Society