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

2017/09/11 by Dyda, Bartłomiej, Lehrbäck, Juha, Vähäkangas, Antti V. · 1 citation
#46E35 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 35A23 #Secondary 26D10

paper · doi:10.48550/arxiv.1709.03296

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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