# Questions tagged [besov-spaces]

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24
questions

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43 views

### Box counting dimension and Besov spaces on $\mathbb R^2$

I found a lemma in this paper of Constantin and Wu, stated with no proof:
Lemma
3.2. Let $b=\chi_{D}$ be the characteristic function of a bounded domain $D\subset\mathbb R^2$ whose boundary has box-...

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34 views

### Besov or Triebel-Lizorkin spaces versus Lorentz spaces

I first asked this question on math.stackexchange here but it seems it is more a research level question ...
At the $0$ order of derivatives of Sobolev spaces and for a fixed integrability order $p$, ...

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47 views

### Space contained in the Interpolation of $L^\infty$ and the Wiener Algebra $\mathcal{F}(L^1)$

Let $\ell^p$ be the space of sequences with power $p$ summable to $\ell^\infty$, $L^p = L^p(\mathbb{R^d})$ be the Lebesgue spaces and $\mathcal{F}$ be the Fourier $d$-dimensional Fourier transform.
...

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47 views

### Embedding of anisotropic Besov Spaces in spaces of continuous/differentiable functions

I am interested in anisotropic Besov spaces. In particular I am interested in the embedding of such anisotropic Besov spaces into possibly anisotropic spaces of differentiable functions.
$\newcommand{...

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142 views

### Why is this estimate about Besov norms true

For reference, I am reading the paper "Uniqueness of Finite Energy Solutions for Maxwell-Dirac and Maxwell-Klein-Gordon Equations" by Masmoudi and Nakanishi.
Let $A_0$ be a scalar function satisfying ...

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104 views

### Characterization of Besov space with Lp-modulus of continuity

When reading the characterization of Besov space with $L_p$-modulus of continuity in the 7th chapter “Fractional Order Space” of Sobolev space written by Adams(Page 243), I encounter some small ...

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73 views

### Fractional Hajłasz-Besov-like similar to the Korevaar-Schoen-Sobolev spaces?

Suppose that $(X,\mu,d)$ and $(Y,\nu,\rho)$ are doubling metric measure spaces. Fix $\alpha>0$ and define the space, analogously to this paper, as the collection of all measurable functions $f:X\...

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72 views

### Choosing the weight in a particular definition of Besov spaces

Following Giovanni Leoni's excellent book (or the Wikipedia article) one possible way to define the Besov spaces $B^{s,p,\theta}(\mathbb R ^d)$, with $s\in(0,1)$ the fractional "order of derivative" ...

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161 views

### Injection of Besov spaces in $L^p$

I believe that for $p\ge 2$, we have the continuous injection (for $p=2$, it is an equality),
$$
B^0_{p,2}(\mathbb R^n)\subset L^p(\mathbb R^n),
$$
where $B^0_{p,2}(\mathbb R^n)$ is the Besov space.
...

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55 views

### Sharp asymptotic behavior of the metric entropy for the unit ball in Besov space

For $s>0$ and $1 \leq p,q \leq \infty$ let $B^s_{p,q}$ be the Besov space defined on $[0,1]^d$, and assume $ s > d( \frac 1 p - \frac 1 2)_+$, such that $B^s_{p,q}$ is compactly embedded in $L^2(...

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161 views

### Estimate of the difference quotients in terms of an $L^{1,\infty}$ function

Let $f \colon \mathbb R^d \to \mathbb R$ be a measurable function. Consider the following property:
(P) there exist a negligible set $N \subset \mathbb R^d$ and function $T_f \in L^p(\mathbb R^d)$ ...

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**1**answer

127 views

### Relation between a norm and norm of Besov spaces

Let $(H, \|\cdot\|)$ be a Hilbert space, $A \colon D(A)\subset H \longrightarrow H$ generates an analytic semigroup $T(t)$ on $H$. We define the following Banach space with the respect norm
$$F=\{x\in ...

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126 views

### Hölder-Zygmund spaces of negative order

In the equation (1.1.17) in Proposition 1.1.6 (ii) in Alazard and Delort's Sobolev Estimates for Two Dimensional Water Waves, there appears a norm named $C^{-1}$, but in Chapter 6 (Appendix) of the ...

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51 views

### Generalized Besov spaces with different integrability and smoothness in space and time?

Consider the family of Besov spaces $B_{p,q}^{s}(\mathbb{R})$ with $0<p,q \leq \infty$ and $s \in \mathbb{R}$.
Is there a natural way to define spaces of generalized functions $f(t,x) \in \mathcal{...

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188 views

### An inequality from Bessel potential space to Besov space

I'm not sure this question is suitable for MathOverflow. Currently, I'm reading a paper "Inhomogeneous Dirichlet Problem in Lipschitz domain" by Jerison and Kenig.
I have a question on some ...

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35 views

### Continuous mapping on Besov spaces?

Consider $f\in B_{p,q}^s(\Omega)$, $\Omega$ compact in $\mathbb{R}^d$, with $p,q\geq 1$ and $s>d/p$ (so the elements in the space are regular enough to be continuous functions), such that $\|f\|_{...

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303 views

### “Reversion” of class $J(\theta)$ interpolation property for Besov spaces

In (function space) interpolation theory, a Banach space $E$ is of class $J(\theta)$ (for $0 < \theta < 1$) if $$X \cap Y \subseteq E \subseteq X+Y,$$ where $(X,Y)$ are Banach spaces and form an ...

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96 views

### Imbedding Theorems between Besov Spaces and space of continuos functions on the unit circle

I'll try to be brief.
Let us consider the Besov Space $B^{1/p}_{p, p}(\mathbb{T})$, where $1\leq p<\infty $ and $\mathbb{T}$ is the unit circle in the complex plane. I would like to know for which ...

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128 views

### Besov regularity of càdlàg functions?

Let $D(\mathbb{R})$ be the space of functions from $\mathbb{R}$ to $\mathbb{R}$ that are right continuous with left limits (also referred to as càdlàg functions). $D(\mathbb{R})$ is often called the ...

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285 views

### Embeddings between weighted Besov spaces

Consider the Besov spaces $B_{p,q}^s(\mathbb{R}^d)$ for parameters $0<p,q\leq \infty$ and $s\in \mathbb{R}$. The weighted Besov space $B_{p,q}^s(\mathbb{R}^d;\mu)$ is defined for $\mu \in \mathbb{R}...

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337 views

### Are Sobolev trace spaces equal from both sides of the boundary?

Let $\Omega\subset\mathbb R^n$ be a bounded open set and $\Omega'$ the complement of its closure.
Assume $\partial\Omega=\partial\Omega'$.
Are the quotient spaces $W^{1,p}(\Omega)/W^{1,p}_0(\Omega)$ ...

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**1**answer

2k views

### Besov and Triebel-Lizorkin spaces

Let me start with a couple of notational reminders. For $\xi\in \mathbb R^n$,
$$
1=\varphi_{0}(\xi)+\sum_{\nu \ge 1}\varphi_{\nu}(\xi),\quad \varphi_{0}\in C^\infty_c(\mathbb R^{n}),\quad \varphi_{\nu}...

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143 views

### Real interpolation space between the Wiener algebra and $L^2$

The Wiener algebra $W_n$ is the image by the Fourier transform of $L^1(\mathbb R^n)$. What is the (complex) interpolation space between $W_n$ and $L^2(\mathbb R^n)$? It is probably not true that for $\...

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251 views

### Reference request : Besov spaces on ubounded domains

As I am relatively new to these matters, I would like to know if you could provide me a reference for Besov spaces on unbounded domains, because when I checked the first tome of Triebel's Theory of ...