Geodesic
Uniformly convergent Fourier series and multiplication of functions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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. 
V. V. Lebedev. Uniformly convergent Fourier series and multiplication of functions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 186-192. http://geodesic.mathdoc.fr/item/TM_2018_303_a13/
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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/TM_2018_303_a13/}
}
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