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.