Widths of Embeddings of Weighted Wiener Classes

In this paper we will study the asymptotic behaviour of certain widths of the embeddings $ mathcal{A}_omega(mathbb{T}^d) to L_p(mathbb{T}^d)$, $2le p le infty$, and $ mathcal{A}_omega(mathbb{T}^d) to mathcal{A}(mathbb{T}^d)$, where $mathcal{A}_{omega}(mathbb{T}^d)$ is the weighted Wiener class and $mathcal{A}(mathbb{T}^d)$ is the Wiener algebra on the $d$-dimensional torus $mathbb{T}^d$. Our main interest will consist in the calculation of the associated asymptotic constant. As one of the consequences we also obtain the asymptotic constant related to the embedding $id: C^m_{rm mix}(mathbb{T}^d) to L_2(mathbb{T}^d)$ for Weyl and Bernstein numbers.