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July, 2019 Superharmonic functions of Schrödinger operators and Hardy inequalities
Yusuke MIURA
J. Math. Soc. Japan 71(3): 689-708 (July, 2019). DOI: 10.2969/jmsj/79597959

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.

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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

Information

Received: 14 January 2018; Published: July, 2019
First available in Project Euclid: 4 April 2019

zbMATH: 07121549
MathSciNet: MR3985615
Digital Object Identifier: 10.2969/jmsj/79597959

Subjects:
Primary: 31C25
Secondary: 31C05, 60J25

Rights: Copyright © 2019 Mathematical Society of Japan

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Vol.71 • No. 3 • July, 2019
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