  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.
