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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Multipliers of $ L\sp p\sb E$. I


Author: Daniel M. Oberlin
Journal: Trans. Amer. Math. Soc. 221 (1976), 187-198
MSC: Primary 43A22
DOI: https://doi.org/10.1090/S0002-9947-1976-0402417-9
MathSciNet review: 0402417
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Abstract: Let X be an abelian group, the character group of a compact group G. For a subset E of X let $ L_E^p$ be the subspace of E-spectral functions in $ {L^p}(G)$. We show that if X is infinite and $ 1 \leqslant p < 2$, then E can be chosen so that not every multiplier of $ \widehat{L_E^p}$ extends to a multiplier of $ \widehat{{L^p}}(G)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0402417-9
Keywords: Multiplier, translation invariant subspace of $ {L^p}(G)$
Article copyright: © Copyright 1976 American Mathematical Society