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
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{TM_2018_303_a13,
author = {V. V. Lebedev},
title = {Uniformly convergent {Fourier} series and multiplication of functions},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {186--192},
publisher = {mathdoc},
volume = {303},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TM_2018_303_a13/}
}
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/