Orlicz-Besov延拓域和Ahlfors n-正则域

Orlicz-Besov extension and Ahlfors n-regular domains

设n≥2,以及?:[0,∞)→[0,∞)为Young函数且满足条件sup t>0∫t 0 t^(n)φ(s)ds/φ(t)s^(n)s<∞.对任意区域Ω⊂R^(n),该条件保证了Besov-Orlicz空间B^(φ)(Ω)是非平凡的.本文证明Ahlfors n-正则域是Besov-Orlicz B^(φ)-延拓域.相反地,进一步假设φ在∞处满足次指数增长条件,本文证明Besov-Orlicz B^(φ)-延拓域是Ahlfors n-正则域.

Let n>2 andϕ:[0,∞)→[0,∞)be a Young function satisfying sup t>0∫t 0 t^(n)φ(s)ds/φ(t)s^(n)s<∞,which guarantees the non-triviality of Besov-Orlicz spaces B^(ϕ)(Ω)in any domainΩ⊂R^(n).In this paper,we prove that Ahlfors n-regular domains must be Besov-Orlicz B^(ϕ-)extension domains.Conversely,assuming additionally thatϕgrows sub-exponentially at∞,we prove that Besov-Orlicz B^(ϕ)-extension domains must be Ahlfors n-regular domains.