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

Lau, Ka-Sing

doi:10.1090/S0002-9947-1983-0694372-5

Extension of Wiener’s Tauberian identity and multipliers on the Marcinkiewicz space
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Trans. Amer. Math. Soc. 277 (1983), 489-506 Request permission

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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