Inegalités de Sobolev Pour les Sous Laplaciens de Certains Groupes Unimodulaires.
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N. Lohoué (1992)
Geometric and functional analysis
Jacek Zienkiewicz (1997)
Studia Mathematica
Let L be the full laplacian on the Heisenberg group of arbitrary dimension n. Then for such that , s > 3/4, for a we have . On the other hand, the above maximal estimate fails for s < 1/4. If Δ is the sublaplacian on the Heisenberg group , then for every s < 1 there exists a sequence and such that and for a we have .
Plotnikova, E.A. (2008)
Sibirskij Matematicheskij Zhurnal
Gérard Schiffmann (1971)
Bulletin de la Société Mathématique de France
Michalis Anoussis (1992)
Bulletin de la Société Mathématique de France
Abderrazak Bouaziz (1994)
Annales scientifiques de l'École Normale Supérieure
Joanne Erdman Snow (1990)
Manuscripta mathematica
Fulton B. Gonzalez (1990)
Mathematische Annalen
G. van Dijk (1984)
Mathematische Annalen
G. C. M. Ruitenburg (1989)
Compositio Mathematica
Toshiyuki Kobayashi (1997)
Journal für die reine und angewandte Mathematik
Robert S. Strichartz (1972)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Arnal, Didier, Boukary Baoua, Oumarou, Benson, Chal, Ratcliff, Gail (2001)
Journal of Lie Theory
Khaoua, Abderrahim (1998)
Journal of Lie Theory
Rory Biggs (2017)
Communications in Mathematics
We investigate the isometry groups of the left-invariant Riemannian and sub-Riemannian structures on simply connected three-dimensional Lie groups. More specifically, we determine the isometry group for each normalized structure and hence characterize for exactly which structures (and groups) the isotropy subgroup of the identity is contained in the group of automorphisms of the Lie group. It turns out (in both the Riemannian and sub-Riemannian cases) that for most structures any isometry is the...
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