| Abstrakt: |
Let Ω be a bounded non-smooth domain in R n that satisfies the measure density condition. In this paper, the authors study the interrelations of three basic types of Besov spaces B p , q s (Ω) , B ˚ p , q s (Ω) and B ~ p , q s (Ω) on Ω , which are defined, respectively, via the restriction, completion and supporting conditions with p , q ∈ [ 1 , ∞) and s ∈ (0 , 1) . The authors prove that B p , q s (Ω) = B ˚ p , q s (Ω) = B ~ p , q s (Ω) , if Ω supports a fractional Besov–Hardy inequality, where the latter is proved under certain conditions on fractional Besov capacity or Aikawa's dimension of the boundary of Ω . [ABSTRACT FROM AUTHOR] |
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