Weighted fractional Poincaré-type inequalities are proved on John domains whenever the weights defined on the domain depend on the distance to the boundary and to an arbitrary compact set in the boundary of the domain.
We establish fractional Hardy-type inequalities in a bounded domain with plump complement. In particular our results apply in bounded C ∞ domains and Lipschitz domains. Date: November 20, 2018. 2010 Mathematics Subject Classification. 46E35 (26D10). Key words and phrases. fractional Hardy-type inequality, domain with plump complement, Lipschitz domain, C ∞ domain.A.
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