Let $nge2$ and $phi : [0,fz) to [0,infty)$ be a Youngs function satisfying $sup_{x>0} int_0^1frac{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, w
hich 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.
In this paper, we study the Sobolev extension property of Lp-quasidisks which are the generalizations of the classical quasidisks. After that, we also find some applications of their Sobolev extension property.
We study extensions of Sobolev and BV functions on infinite-dimensional domains. Along with some positive results we present a negative solution of the long-standing problem of existence of Sobolev extensions of functions in Gaussian Sobolev spaces from a convex domain to the whole space.
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We show that the first order Sobolev spaces on cuspidal symmetric domains can be characterized via pointwise inequalities. In particular, they coincide with the Hajlasz-Sobolev spaces.