Geodesic
Uniformly convergent Fourier series and multiplication of functions
Informatics and Automation, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 186-192.

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Let $U(\mathbb T)$ be the space of all continuous functions on the circle $\mathbb T$ whose Fourier series converges uniformly. Salem's well-known example shows that a product of two functions in $U(\mathbb T)$ does not always belong to $U(\mathbb T)$ even if one of the factors belongs to the Wiener algebra $A(\mathbb T)$. In this paper we consider pointwise multipliers of the space $U(\mathbb T)$, i.e., the functions $m$ such that $mf\in U(\mathbb T)$ whenever $f\in U(\mathbb T)$. We present certain sufficient conditions for a function to be a multiplier and also obtain some Salem-type results.
Keywords: uniformly convergent Fourier series, function spaces, multiplication operators. 
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     author = {V. V. Lebedev},
     title = {Uniformly convergent {Fourier} series and multiplication of functions},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2018_303_a13/}
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V. V. Lebedev. Uniformly convergent Fourier series and multiplication of functions. Informatics and Automation, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 186-192. http://geodesic.mathdoc.fr/item/TRSPY_2018_303_a13/

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