# Questions tagged [besov-space]

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

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### Can I control the Lp norm of a difference quotient of a suitable Besov function with a finite constant (or norm)?

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### How to show the lifting property of an operator described in its ellipticity

Consider Soblev spaces as special cases of Besov spaces characterized by wavelets, $H^s = B^s_{2,2}$. I want to prove the following statement. For a positive definite self-adjoint operator $A$, if ...
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### 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 ...
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### Reference request on Besov spaces and bounded variation functions.

Would someone have any good references which address Besov spaces, and functions of bounded variations. I don't know anything about theses spaces so I am looking for something that would introduce me ...
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### 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 ...
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### Besov spaces---concrete description of spatial inhomogeneity

Some very pedestrian questions about Besov spaces. Just to fix notation: 1.Let $f \in \mathcal{S}'$, the space of tempered distributions. 2.$\Psi, \{ \Phi_n \}_{n \geq 0} \subset \mathcal{S}$ such ...
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### Closure of Schwartz space in homogeneous Besov space

Let $\dot{B}^s_{\infty,\infty}(\mathbb{R}^d)$ denote the homogeneous Besov space of order $s$ with second and third index $\infty$, i. e. the homogeneous Zygmund space. Let $\mathcal{S}(\mathbb{R}^d)$ ...
For $1\leq p\leq\infty$, the $r$-th order $L^p$-modulus of smoothness is \begin{equation} \omega_r(u,t,\Omega)_p=\sup_{|h|\leq t}\|\Delta_h^ru\|_{L^p(\Omega_{rh})} \end{equation} where $\Omega_{rh}=\{... 1answer 994 views ### Functions on Besov spaces and Hölder conditions Consider$f_1(x)=-1/\log(|x|)$and$f_2(x)=1/\sqrt{-\log(|x|)}$around$x=0$. It can be shown, just by contradiction, that the previous functions do not verify any (positive) Hölder condition:$$|... 1answer 829 views ### Dense subspace of Zygmund space or Hölder space? Do we know any function spaces dense in Zygmund space$C_*^s$(a special case of Besov space, i.e.$C_*^s = B^s_{\infty,\infty}$) or Hölder space$C^{k,r}$, with underlying field$\mathbb{R}^d$? Will$...
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 ...