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

 

Multipliers of weak type
on locally compact Vilenkin groups


Author: T. S. Quek
Journal: Proc. Amer. Math. Soc. 124 (1996), 2727-2736
MSC (1991): Primary 43A22; Secondary 43A15, 43A70
MathSciNet review: 1327041
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Abstract: Let $G$ be a locally compact Vilenkin group with dual group $\Gamma $. We give a sufficient condition for $f\in L^\infty (\Gamma )$ to be a multiplier of weak type $(p,p)$ on $G$. Some applications of our result are given. We also prove that our result is sharp.


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Additional Information

T. S. Quek
Affiliation: Department of Mathematics, National University of Singapore, Singapore 0511, Republic of Singapore

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03365-5
PII: S 0002-9939(96)03365-5
Keywords: Vilenkin groups, Fourier multipliers, Lipschitz spaces
Received by editor(s): November 28, 1994
Received by editor(s) in revised form: February 28, 1995
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society