Nonfactorization of functions in Banach subspaces of $L^{1}(G)$
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- by Leonard Y. H. Yap PDF
- Proc. Amer. Math. Soc. 51 (1975), 356-358 Request permission
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.References
- J. T. Burnham, Nonfactorization in subsets of the measure algebra, Proc. Amer. Math. Soc. 35 (1972), 104โ106. MR 298342, DOI 10.1090/S0002-9939-1972-0298342-9 R. Larsen, The algebras of functions with Fourier transforms in ${L_p}$: A survey, University of Oslo, 1973, (preprint).
- John C. Martin and Leonard Y. H. Yap, The algebra of functions with Fourier transforms in $L^{p}$, Proc. Amer. Math. Soc. 24 (1970), 217โ219. MR 247378, DOI 10.1090/S0002-9939-1970-0247378-0
- Hwai Chiuan Wang, Nonfactorization in group algebras, Studia Math. 42 (1972), 231โ241. MR 303217, DOI 10.4064/sm-42-3-231-241
- Leonard Y. H. Yap, Ideals in subalgebras of the group algebras, Studia Math. 35 (1970), 165โ175. MR 270075, DOI 10.4064/sm-35-2-165-175
Additional Information
- © Copyright 1975 American Mathematical Society
- 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