Hardy inequalities with optimal constants and remainder terms
Hardy inequalities with optimal constants and remainder terms
We show that the classical Hardy inequalities with optimal constants in the Sobolev spaces $W_0^{1,p}$ and in higher-order Sobolev spaces on a bounded domain $\Omega \subset \mathbb {R}^n$ can be refined by adding remainder terms which involve $L^p$ norms. In the higher-order case further $L^p$ norms with lower-order singular weights …