Fractional Hardy–Sobolev type inequalities for half spaces and John domains

Dyda, Bartłomiej; Lehrbäck, Juha; Vähäkangas, Antti

doi:10.1090/proc/14051

Fractional Hardy–Sobolev type inequalities for half spaces and John domains
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by Bartłomiej Dyda, Juha Lehrbäck and Antti V. Vähäkangas PDF

Proc. Amer. Math. Soc. 146 (2018), 3393-3402 Request permission

Abstract:

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.

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