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Pietro Majer
Pietro Majer
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Yes, it is HolderHölder spaces and can be regarded as SS spaces for $p=\infty$. Actually, for natural $\mu$ more correct for functions analysis are Zygmund spaces (with differences of th second order in the definition). They are special cases of Besov spaces, which are defined for $0 < p\le \infty$, $\mu\in \mathbb R$. They coincide with corresponding Sobolev-Slobodetskij in some cases. But there are some differences between cases $p<\infty$ and $p=\infty$. For example, Holder spaces are not separable.

On the second question, shown what? It is a definition for $p=\infty$.

Yes, it is Holder spaces and can be regarded as SS spaces for $p=\infty$. Actually, for natural $\mu$ more correct for functions analysis are Zygmund spaces (with differences of th second order in the definition). They are special cases of Besov spaces, which are defined for $0 < p\le \infty$, $\mu\in \mathbb R$. They coincide with corresponding Sobolev-Slobodetskij in some cases. But there are some differences between cases $p<\infty$ and $p=\infty$. For example, Holder spaces are not separable.

On the second question, shown what? It is a definition for $p=\infty$.

Yes, it is Hölder spaces and can be regarded as SS spaces for $p=\infty$. Actually, for natural $\mu$ more correct for functions analysis are Zygmund spaces (with differences of th second order in the definition). They are special cases of Besov spaces, which are defined for $0 < p\le \infty$, $\mu\in \mathbb R$. They coincide with corresponding Sobolev-Slobodetskij in some cases. But there are some differences between cases $p<\infty$ and $p=\infty$. For example, Holder spaces are not separable.

On the second question, shown what? It is a definition for $p=\infty$.

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Andrew
Andrew
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Yes, it is Holder spaces and can be regarded as SS spaces for $p=\infty$. Actually, for natural $\mu$ more correct for functions analysis are Zygmund spaces (with differences of th second order in the definition). They are special cases of Besov spaces, which are defined for $0<p\le \infty$$0 < p\le \infty$, $\mu\in \mathbb R$. They coincide with corresponding Sobolev-Slobodetskij in some cases. But there are some differences between cases $p<\infty$ and $p=\infty$. For example, Holder spaces are not separable.

On the second question, shown what? It is a definition for $p=\infty$.

Yes, it is Holder spaces and can be regarded as SS spaces for $p=\infty$. Actually, for natural $\mu$ more correct for functions analysis are Zygmund spaces (with differences of th second order in the definition). They are special cases of Besov spaces, which are defined for $0<p\le \infty$, $\mu\in \mathbb R$. They coincide with corresponding Sobolev-Slobodetskij in some cases. But there are some differences between cases $p<\infty$ and $p=\infty$. For example, Holder spaces are not separable.

On the second question, shown what? It is a definition for $p=\infty$.

Yes, it is Holder spaces and can be regarded as SS spaces for $p=\infty$. Actually, for natural $\mu$ more correct for functions analysis are Zygmund spaces (with differences of th second order in the definition). They are special cases of Besov spaces, which are defined for $0 < p\le \infty$, $\mu\in \mathbb R$. They coincide with corresponding Sobolev-Slobodetskij in some cases. But there are some differences between cases $p<\infty$ and $p=\infty$. For example, Holder spaces are not separable.

On the second question, shown what? It is a definition for $p=\infty$.

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Andrew
Andrew
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Yes, it is Holder spaces and can be regarded as SS spaces for $p=\infty$. Actually, for natural $\mu$ more correct for functions analysis are Zygmund spaces (with differences of th second order in the definition). They are special cases of Besov spaces, which are defined for $0<p\le \infty$, $\mu\in \mathbb R$. They coincide with corresponding Sobolev-Slobodetskij in some cases. But there are some differences between cases $p<\infty$ and $p=\infty$. For example, Holder spaces are not separable.

On the second question, shown what? It is a definition for $p=\infty$.