Nuclear Fourier Transforms

The paper deals with the problem under which conditions for the parameters s(1), s(2) is an element of R, 1 <= p, q(1), q(2) <= infinity the Fourier transform F is a nuclear mapping from A(p,q1)(s1) (R-n) into A(p,q2)(s2) (R-n), where A is an element of {B, F} stands for a space of Besov or Triebel-Lizorkin type, and n is an element of 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 F acting in the same type of spaces was studied.

Automated summary

The paper investigates the conditions under which the Fourier transform F is a nuclear mapping from A(p,q1)(s1) (R-n) to A(p,q2)(s2) (R-n), where s(1) and s(2) are real parameters, and 1 <= p, q(1), q(2) <= infinity. The spaces A represent Besov or Triebel-Lizorkin types, and n is a natural number. It extends the recent paper 'Mapping properties of Fourier transforms' by the third-named author, which studied the compactness of F in the same type of spaces.