Superharmonic functions of Schrodinger operators and Hardy inequalities

摘要

Given a Dirichlet form with generator L and a measure μ, we consider superharmonic functions of the Schrodinger operator L + μ. We probabilistically prove that the existence of superharmonic functions gives rise to the Hardy inequality. More precisely, the L~2-Hardy inequality is derived from Itô's formula applied to the superharmonic function.