Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orlicz-Besov extension and Ahlfors $n$-regular domains   Let $n\ge2$ and $\phi : [0,\fz) \to [0,\infty)$ be a
  Young's function satisfying $\sup_{x>0} \int_0^1\frac{\phi( t x)}{
\phi(x)}\frac{dt}{t^{n+1} }<\infty. $
  We show that Ahlfors $n$-regular domains are Besov-Orlicz ${\dot {\bf
B}}^{\phi}$ extension domains,
  which is necessary to guarantee the nontrivially of ${\dot {\bf B}}^{\phi}$.
On the other hand, assume that $\phi$ grows sub-exponentially at $\fz$
additionally. If $\Omega$ is a Besov-Orlicz ${\dot {\bf B}}^{\phi}$ extension
domain, then it must be Ahlfors $n$-regular.

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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: stat