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Transactions of the American Mathematical Society

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Extension of Wiener's Tauberian identity and multipliers on the Marcinkiewicz space


Author: Ka-Sing Lau
Journal: Trans. Amer. Math. Soc. 277 (1983), 489-506
MSC: Primary 42A45; Secondary 42A38
MathSciNet review: 694372
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Abstract: This is a continuation of the work of Bertrandias, Lee and Lau on Wiener's generalized harmonic analysis. Among the other results, we extend Wiener's Tauberian identity to cover a larger class of functions; we characterize the multipliers on the Marcinkiewicz space $ {\mathcal{M}^2}$, and we obtain a Tauberian theorem on $ {\mathcal{M}^2}$ with full generality.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0694372-5
Article copyright: © Copyright 1983 American Mathematical Society