Abstract

We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators $L_pu:=-\nabla _L^*$. If $\phi $ is a positive weight such that $-L_p\phi \ge 0$, then the Hardy-type inequalityholds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups