A fractional order Hardy inequality
A fractional order Hardy inequality
We investigate the following integral inequality: \[ \int_D \frac{|u(x)|^p}{\dist(x, D^c)^\alpha} dx \leq c \int_D \!\int_D \frac{|u(x)-u(y)|^p}{|x-y|^{d+\alpha}} dx\,dy, \quad u\in C_c(D), \] where $\alpha,p>0$ and $D\subset \Rd$ is a Lipschitz domain or its complement or a complement of a point.