Fractional Hardy-Sobolev type inequalities for half spaces and John domains. (arXiv:1709.03296v1 [math.CA])

As our main result we prove a variant of the fractional Hardy-Sobolev-Maz'ya inequality for half spaces. This result contains a complete answer to a recent open question by Musina and Nazarov. In the proof we apply a new version of the fractional Hardy-Sobolev inequality that we establish also for more general unbounded John domains than half spaces. 查看全文>>