Fractional Besov spaces and Hardy inequalities on bounded non-smooth domains

Let Omega 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) (Omega), (B)(p,q)(s) (Omega)and B-p,q(s )(Omega) on Omega, which are defined, respectively, via the restriction, completion and supporting conditions with p,q is an element of [1,infinity) and s is an element of (0,1). The authors prove that B-p,q(s) (Omega) = (B)(p,q)(s) (Omega)= B-p,q(s) (Omega), if Omega 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 Omega.