Nuclear Fourier Transforms

Abstract

The paper deals with the problem under which conditions for the parameters $$s_1,s_2\in \mathbb R$$ s 1 , s 2 ∈ R , $$1\le p,q_1,q_2\le \infty $$ 1 ≤ p , q 1 , q 2 ≤ ∞ the Fourier transform $$\mathcal {F}$$ F is a nuclear mapping from $$A^{s_1}_{p,q_1}({\mathbb R}^n)$$ A p , q 1 s 1 ( R n ) into $$A^{s_2}_{p,q_2}({\mathbb R}^n)$$ A p , q 2 s 2 ( R n ) , where $$A\in \{B,F\}$$ A ∈ { B , F } stands for a space of Besov or Triebel–Lizorkin type, and $$n\in \mathbb N$$ n ∈ N . It extends the recent paper ‘Mapping properties of Fourier transforms’ (Triebel in Z Anal Anwend 41(1/2):133–152, https://doi.org/10.4171/ZAA/1697, 2022) by the third-named author, where the compactness of $$\mathcal {F}$$ F acting in the same type of spaces was studied.