Traces of Besov and Lizorkin--Triebel spaces to thick subsets of $\mathbb{R}^n$

RESUMO

Let $d\in [0, n]$ and let $E\subset \mathbb{R}^n$ be a closed $d$-thick set. Given $p\in [1, \infty]$, $q\in (0, \infty]$, and $s\in (\frac{n-d}{p}, 1)$, we provide an intrinsic description of the trace-space of the Besov space $B^s_{p, q}(\mathbb{R}^n)$ to $E$. If, in addition, $p<\infty$, we give an intrinsic description of the trace-space of the Lizorkin--Triebel space $F^s_{p, q}(\mathbb{R}^n)$ to $E$.