Nonintegrability of superharmonic functions
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- by Noriaki Suzuki PDF
- Proc. Amer. Math. Soc. 113 (1991), 113-115 Request permission
Abstract:
In this article we prove the following: If $u$ is a nonzero superharmonic function on a proper subdomain $D$ in ${R^n}$, then \[ {\int _D {\left | {u(x)} \right |} ^p}{\delta _D}{(x)^{np - n - 2p}}dx = \infty ,\] where $0 < p \leq 1$ and ${\delta _D}(x)$ denotes the distance between $x$ and the boundary of $D$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 113-115
- MSC: Primary 31B05
- DOI: https://doi.org/10.1090/S0002-9939-1991-1054163-2
- MathSciNet review: 1054163