Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A Liouville-type theorem on halfspaces
for the Kohn Laplacian

Author: Francesco Uguzzoni
Journal: Proc. Amer. Math. Soc. 127 (1999), 117-123
MSC (1991): Primary 31C05, 31B05, 35J15
MathSciNet review: 1458268
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Abstract: Let $\Delta _{ \mathbb{H}^{n}}$ be the Kohn Laplacian on the Heisenberg group $ \mathbb{H}^{n}$ and let $\Omega$ be a halfspace of $ \mathbb{H}^{n}$ whose boundary is parallel to the center of $ \mathbb{H}^{n}$. In this paper we prove that if $u$ is a non-negative $\Delta _{ \mathbb{H}^{n}}$-superharmonic function such that

\begin{displaymath}u\in L^{1}(\Omega),\end{displaymath}

then $u\equiv 0$ in $\Omega$.

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Additional Information

Francesco Uguzzoni
Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy

Keywords: Heisenberg group, Kohn Laplacian, superharmonic functions, halfspaces
Received by editor(s): February 18, 1997
Received by editor(s) in revised form: April 30, 1997
Communicated by: Jeffrey B. Rauch
Article copyright: © Copyright 1999 American Mathematical Society