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Register a new userFractional Orlicz-Sobolev extension/imbedding on Ahlfors $n$-regular domains
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Tian Liang
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In this paper we build up a criteria for fractional Orlicz-Sobolev extension and imbedding domains on Ahlfors $n$-regular domains.
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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, 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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