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Proceedings of the American Mathematical Society

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

 

 

Nonfactorization of functions in Banach subspaces of $ L\sp{1}(G)$


Author: Leonard Y. H. Yap
Journal: Proc. Amer. Math. Soc. 51 (1975), 356-358
MSC: Primary 43A15
DOI: https://doi.org/10.1090/S0002-9939-1975-0404986-6
MathSciNet review: 0404986
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Abstract: In this note we first prove a theorem on factorization of functions in certain subsets of $ {L^1}(G)$, where $ G$ is a nondiscrete locally compact Abelian group with dual group $ \hat G$. One of the corollaries of this theorem answers a question of R. Larsen concerning the algebras of functions with Fourier transforms in $ {L^p}(\hat G)$. The other corollaries contain nonfactorization results which sharpen some known theorems.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0404986-6
Keywords: Locally compact Abelian groups, subspaces of group algebras, convolution, factorization of functions, Segal algebras
Article copyright: © Copyright 1975 American Mathematical Society