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

Bartłomiej Dyda, Lizaveta Ihnatsyeva, Juha Lehrbäck +2

Let $X$ be a metric space equipped with a doubling measure. We consider weights $w(x)=\mathrm{dist}(x,E{)}^{-\alpha }$, where $E$ is a closed set in $X$ and $\alpha \in \mathbb{R}$. We estab…