On the interpolation space (Lp(Ω),W1,p(Ω))s,p in non-smooth domains

Abstract

We show that, for certain non-smooth bounded domains Ω ⊂ Rn, the real interpolation space (Lp(Ω), W1,p(Ω))s,p is the subspace Ws,p(Ω) ⊂ Lp(Ω) induced by the restricted fractional seminorm |f| Ws,p(Ω) = ∫ Ω ∫ |x−y|< d(x) 2 |f(x) − f(y)| p |x − y|n+sp dy dx) 1 p .