Nuclear Fourier Transforms

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