论文标题
核傅立叶变换
Nuclear Fourier transforms
论文作者
论文摘要
本文处理了参数的条件$ s_1，s_2 \ in \ mathbb {r} $，$ 1 \ leq p，q_1，q_1，q_2 \ leq \ infty $ fourier transform $ \ mathcal {f} $是来自一个核映射的问题。 $ a^{s_1} _ { $ n \ in \ mathbb {n} $。它扩展了最近的论文Arxiv：2112.04896，其中研究了$ \ Mathcal {f} $的紧凑性在同一类型的空间中作用。
The paper deals with the problem under which conditions for the parameters $s_1,s_2\in\mathbb{R}$, $1\leq p,q_1,q_2\leq\infty$ the Fourier transform $\mathcal{F}$ is a nuclear mapping from $A^{s_1}_{p,q_1}(\mathbb{R}^n)$ into $A^{s_2}_{p,q_2}(\mathbb{R}^n)$, 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.
