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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A Liouville-type theorem on halfspaces for the Kohn Laplacian
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by Francesco Uguzzoni PDF
Proc. Amer. Math. Soc. 127 (1999), 117-123 Request permission

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 \[ u\in L^{1}(\Omega ),\] 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
  • Email: uguzzoni@dm.unibo.it
  • Received by editor(s): February 18, 1997
  • Received by editor(s) in revised form: April 30, 1997
  • Communicated by: Jeffrey B. Rauch
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 117-123
  • MSC (1991): Primary 31C05, 31B05, 35J15
  • DOI: https://doi.org/10.1090/S0002-9939-99-04519-0
  • MathSciNet review: 1458268