0000000000617935

AUTHOR

Bartłomiej Dyda

showing 2 related works from this author

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

2018

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.

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_commonProceedings of the American Mathematical Society
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On improved fractional Sobolev–Poincaré inequalities

2016

We study a certain improved fractional Sobolev–Poincaré inequality on domains, which can be considered as a fractional counterpart of the classical Sobolev–Poincaré inequality. We prove the equivalence of the corresponding weak and strong type inequalities; this leads to a simple proof of a strong type inequality on John domains. We also give necessary conditions for the validity of an improved fractional Sobolev–Poincaré inequality, in particular, we show that a domain of finite measure, satisfying this inequality and a ‘separation property’, is a John domain.

Hölder's inequalityKantorovich inequalityPure mathematicsYoung's inequalityBernoulli's inequalityGeneral Mathematics010102 general mathematicsMathematical analysisMinkowski inequality01 natural sciences010101 applied mathematicsLog sum inequalityRearrangement inequality0101 mathematicsCauchy–Schwarz inequalityMathematicsArkiv för Matematik
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