Questions tagged [besov-space]
For questions on Besov spaces, which are complete quasinormal spaces.
3
questions
10
votes
1answer
3k views
Rellich–Kondrachov theorem for traces
Let $W^{1,p}(\Omega)$ be the Sobolev space of weakly differentiable functions whose weak derivatives are $p$-integrable, where $\Omega \subset \mathbb R^n$ is a domain with Lipschitz boundary. Let ...
3
votes
0answers
337 views
Besov–Zygmund spaces and the Inverse Function Theorem, is the Inverse Zygmund?
Preliminary Definitions
Let $\Omega \subset \mathbb{R}^n$ be open. We define the Zygmund spaces $C^r_{*}(\Omega)$ with $r>0$, $r \in \mathbb{R}$ in the following way: (all the functions are ...
2
votes
1answer
110 views
Simple Inequality for Proving Equivalent Besov Seminorms
For $f\in L^{p}(\mathbb{R}^{n})$, $1\leq p<\infty$, and $h\in\mathbb{R}^{n}$, define the quantity
$$I_{p}(h):=\left(\int_{\mathbb{R}^{n}}\left|f(x+h)-f(x)\right|^{p}dx\right)^{1/p}$$
and define ...
