Search results for "Hardy-Sobolev inequality"

showing 2 items of 2 documents

Muckenhoupt $A_p$-properties of distance functions and applications to Hardy-Sobolev -type inequalities

2017

Let $X$ be a metric space equipped with a doubling measure. We consider weights $w(x)=\operatorname{dist}(x,E)^{-\alpha}$, where $E$ is a closed set in $X$ and $\alpha\in\mathbb R$. We establish sharp conditions, based on the Assouad (co)dimension of $E$, for the inclusion of $w$ in Muckenhoupt's $A_p$ classes of weights, $1\le p<\infty$. With the help of general $A_p$-weighted embedding results, we then prove (global) Hardy-Sobolev inequalities and also fractional versions of such inequalities in the setting of metric spaces.

Mathematics::Functional AnalysisMathematics - Analysis of PDEsAssouad dimensionMathematics - Classical Analysis and ODEsmetric spaceHardy-Sobolev inequalityClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematics::Classical Analysis and ODEsMuckenhoupt weight42B25 (Primary) 31E05 35A23 (Secondary)Analysis of PDEs (math.AP)
researchProduct

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
researchProduct