# Questions tagged [besov-space]

For questions on Besov spaces, which are complete quasinormal spaces.

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### Dual of homogeneous Besov space

I am trying to prove a trace theorem from the homogeneous Besov space $\overset{\cdot}{B}_{2,1}^{1/2}(\mathbb{R}^n)$ to $L^2(K)$, where $K$ is a compact euclidean hypersurface. The homogeneous Besov ...
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### Showing a function belongs to a Besov space.

In this paper, just before Theorem 3 it is stated that the kernels given in equations 4a-f are in $\mathbb{B}_{pq}^s$ for all $p,q\geq 1$ and some $s>0$. This is stated without proof/reference and ...
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### Does there exist a function in $B_{\infty,1}^{1/2}\setminus H^{1/2}$?

Does there exist a function in $B_{\infty,1}^{1/2}([0,1])\setminus H^{1/2}([0,1])$? If so can it be constructed explicitly? A reference will be much appreciated.
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### Show that homogeneous distribution of degree $-1$, bounded in $S^2$ satisfies that $\left| S_{0} v(x) \right| \leq \frac{C}{1+ |x|}$

Let $\varphi(x)$ be a rotation-invariant function such that $\varphi \in \mathcal{S}(\mathbb{R}^3)$ (Schwartz space) and \begin{equation} 0 \leq \hat{\varphi}(\xi) \leq 1 , \quad \quad \begin{cases} ...
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### Reference request: Lebesgue/Sobolev spaces on the boundary

I am interested in the Boundary Lebesgue/Sobolev/Besov Spaces $L^p(\partial\Omega;\mathcal{H}^{N-1}), \ W^{k,p}(\partial\Omega),\ B^{s,p}(\partial\Omega)$ where $\Omega\subseteq\mathbb{R}^N$ is a ...
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### Examples of Besov functions of power-logarithmic type $|x|^{\alpha} |\log |x||^{\beta}$

I'm stuck on the following exercise 17.9 from Leoni's text A first course in Sobolev Spaces (second edition). This is from the chapter on Besov spaces, but this is really just a integral inequality ...
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### Does $C_c(X)$ separate points in $X$ when $X$ is a Banach space?

Suppose that $X$ is a separable, infinite dimensional Banach space. We say that a set of functions $\{f_\alpha\}_{\alpha \in A}$ separates points in $X$ if for every $x,y \in X$, there is an $\alpha$...
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### How to prove that a delta function belongs to the Besov space $B^{-1}$?

$\def\R{\mathbb{R}}$ $\DeclareMathOperator{\supp}{supp}$ I am trying to understand the definition of the Besov space and to prove that the delta function in $\R^1$. However I got stuck. First, let ...
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