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Fractional Hardy-Sobolev type inequalities for half spaces and John domains
Bartłomiej DydaAntti V. VähäkangasJuha Lehrbäcksubject
Mathematics::Functional AnalysisPure mathematicsInequalityApplied MathematicsGeneral Mathematicsmedia_common.quotation_subjectta111Mathematics::Classical Analysis and ODEsMathematics::Analysis of PDEsMathematics::Spectral TheoryType (model theory)Sobolev spacefractional Hardy-Sobolev inequalityHardy-Sobolev-Maz'ya inequalityfunktionaalianalyysiepäyhtälötJohn domainsMathematicsmedia_commondescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-04-18 | Proceedings of the American Mathematical Society |