Orlicz-Besov extension and Ahlfors $n$-regular domains
英文摘要：
Let $n\ge2$ and $ϕ: [0,\fz) \to [0,\infty)$ be a Young's function satisfying $\sup_{x>0} \int_0^1\frac{ϕ( t x)}{ ϕ(x)}\frac{dt}{t^{n+1} }<\infty. $ We show that Ahlfors $n$-regular domains are Besov-Orlicz ${\dot {\bf B}}^ϕ$ extension domains, which is necessary to guarantee the nontrivially of ${\dot {\bf B}}^ϕ$. On the other hand, assume that $ϕ$ grows sub-exponentially at $\fz$ additionally. If $Ω$ is a Besov-Orlicz ${\dot {\bf B}}^ϕ$ extension domain, then it must be Ahlfors $n$-regular.
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