Abstract
Given a Dirichlet form with generator $\mathcal{L}$ and a measure $\mu$, we consider superharmonic functions of the Schrödinger operator $\mathcal{L} + \mu$. 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.
Citation
Yusuke MIURA. "Superharmonic functions of Schrödinger operators and Hardy inequalities." J. Math. Soc. Japan 71 (3) 689 - 708, July, 2019. https://doi.org/10.2969/jmsj/79597959
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