Phase-space analysis and pseudodifferential calculus on the Heisenberg group

Details Phase-space analysis and pseudodifferential calculus on the Heisenberg group Phase-space analysis and pseudodifferential calculus on the Heisenberg group

2009-04-30

arxiv.org/abs/0904.4746v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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