Hardy-Sobolev inequalities and weighted capacities in metric spaces

Lizaveta Ihnatsyeva, Juha Lehrbäck, Antti V. Vähäkangas

Let $\Omega$ be an open set in a metric measure space $X$. Our main result gives an equivalence between the validity of a weighted Hardy-Sobolev inequality in $\Omega$ and quasiadditivity of…