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Phase-space analysis and pseudo-differential calculus on the Heisenberg group. (Analyse de l’espace des phases et calcul pseudo-differential sur le groupe de Heisenberg.) (French) Zbl 1178.35020

Summary: We establish pseudo-differential calculus on the Heisenberg group by defining an algebra of operators acting continuously on Sobolev spaces and containing the class of differential operators. Our approach puts into light microlocal directions and completes, with the Littlewood-Paley theory developed by Bahouri et al., a microlocal analysis of the Heisenberg group.

MSC:

35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
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References:

[1] H. Bahouri, C. Fermanian-Kammerer, I. Gallagher, Phase-space analysis and pseudo-differential calculus on the Heisenberg group, 127 pp., soumis; H. Bahouri, C. Fermanian-Kammerer, I. Gallagher, Phase-space analysis and pseudo-differential calculus on the Heisenberg group, 127 pp., soumis · Zbl 1178.35020
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