Abstract
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.
Citation
Bartłomiej Dyda. "A fractional order Hardy inequality." Illinois J. Math. 48 (2) 575 - 588, Summer 2004. https://doi.org/10.1215/ijm/1258138400
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