A fractional order hardy inequality

Abstract

We investigate the following integral inequality: ∫D |u(x)|p/dist(x, Dc)αdx ≤ c ∫ D∫D |u(x) - u(y)|p/|x - y| d+αdx dy, u ∈ Cc(D), where α, p > 0 and D ⊂ ℝd is a Lipschitz domain or its complement or a complement of a point.