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BEURLING AND LIPSCHITZ ALGEBRAS

Published online by Cambridge University Press:  01 November 1999

DAVID LAMB
DAVID LAMB
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT
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Abstract

It is well known that there exist infinite closed subsets E of [ ] such that A(E) = C(E) (see, for example, [3]). Such sets are called Helson sets. Let E be a closed subset of [ ], let 0 < α < 1, and let Aα(E) be the restriction of the Beurling algebra Aα([ ]). Then Aα(E) ⊂ lipαE. We shall show that Aα(E) = lipαE if and only if E is finite. This answers a question raised by Pedersen [5], where partial results were obtained.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 6 , November 1999 , pp. 719 - 721
Copyright
© The London Mathematical Society 1999

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