We investigate the following integral inequality: \[ ∫_D |u(x)|^p/(x, D^c)^α dx ≤ c ∫_D \!∫_D {|u(x)-u(y)|^p}{|x-y|d+α} dx\,dy, u∈ C_c(D), \] where α,p>0 and D⊂ is a Lipschitz domain or its complement or a complement of a point.
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Bartłomiej Dyda (2004) studied this question.