Critical Hardy--Sobolev Inequalities

Abstract

We consider Hardy inequalities in $I{R}^n$, $n\ge 3$, with best constant that involve either distance to the boundary or distance to a surface of co-dimension $k<n$, and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm.

22 pages