Phase-space analysis and pseudodifferential calculus on the Heisenberg group

Hajer Bahouri (1) , Clotilde Fermanian Kammerer (2) , Isabelle Gallagher (3)

1 FST - Faculté des Sciences Mathématiques, Physiques et Naturelles de Tunis
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 IMJ - Institut de Mathématiques de Jussieu

A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those pseudodifferential operators act continuously on Sobolev spaces and the loss of derivatives may be controled by the order of the operator. Although a large number of works have been devoted in the past to the construction and the study of algebras of variable-coefficient operators, including some very interesting works on the Heisenberg group, our approach is different, and in particular puts into light microlocal directions and completes, with the Littlewood-Paley theory developed in~\cite{bgx} and~\cite{bg}, a microlocal analysis of the Heisenberg group.

Domaines: Equations aux dérivées partielles [math.AP]

Hajer Bahouri, Clotilde Fermanian Kammerer, Isabelle Gallagher. Phase-space analysis and pseudodifferential calculus on the Heisenberg group. 2013. ⟨hal-00380110v4⟩