Abstract
AbstractThe 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics,Analysis
Reference26 articles.
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3. Cobos, F., Edmunds, D.E., Kühn, T.: Nuclear embeddings of Besov spaces into Zygmund spaces. J. Fourier Anal. Appl. 26(1), 9 (2020). https://doi.org/10.1007/s00041-019-09709-6
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