6533b874fe1ef96bd12d612e
RESEARCH PRODUCT
Muckenhoupt $A_p$-properties of distance functions and applications to Hardy-Sobolev -type inequalities
Bart��omiej DydaLizaveta IhnatsyevaJuha Lehrb��ckHeli TuominenAntti V. V��h��kangassubject
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)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-05-03 |