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arXiv · 1807.03949

Uniformly convergent Fourier series and multiplication of functions

V. V. Lebedev
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Abstract

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 belongs 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 results of Salem type.

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V. V. Lebedev. 2018-07-11. Uniformly convergent Fourier series and multiplication of functions. https://doi.org/10.1134/s008154381808014x

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