Nuclear Fourier transforms

Abstract

The paper deals with the problem under which conditions for the parameters $s_1,s_2\in \mathbb{R}$, $1\le p,q_1,q_2\le \infty$ the Fourier transform $\mathcal{F}$ is a nuclear mapping from $A_{p,q_1}^{s_1}({\mathbb{R}}^n)$ into $A_{p,q_2}^{s_2}({\mathbb{R}}^n)$, where $A\in \{B,F\}$ stands for a space of Besov or Triebel-Lizorkin type, and $n\in \mathbb{N}$. It extends the recent paper arXiv:2112.04896 where the compactness of $\mathcal{F}$ acting in the same type of spaces was studied.

20 pages, 3 figures