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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterisation of Lipschitz classes on $0$-dimensional groups
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by Walter R. Bloom PDF
Proc. Amer. Math. Soc. 53 (1975), 149-154 Request permission

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
  • 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
  • Walter R. Bloom, Jackson’s theorem for locally compact abelian groups, Bull. Austral. Math. Soc. 10 (1974), 59–66. MR 336227, DOI 10.1017/S0004972700040624
  • 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
  • P. L. Walker, Lipschitz classes on $0$-dimensional groups, Proc. Cambridge Philos. Soc. 63 (1967), 923–928. MR 216246, DOI 10.1017/s0305004100041906
  • A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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