Astérisque 2012; 127 pp; softcover Number: 342 ISBN10: 2856293344 ISBN13: 9782856293348 List Price: US$52 Member Price: US$41.60 Order Code: AST/342
 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 controlled 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 variablecoefficient operators, including some very interesting works on the Heisenberg group, the authors' approach is different, and in particular puts into light microlocal directions and completes, with the LittlewoodPaley theory initiated in 2000 by Bahouri, Gérard, and Xu: a microlocal analysis of the Heisenberg group. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in pure mathematics. Table of Contents  Introduction and main results
 Fundamental properties of pseudodifferential operators
 The algebra of pseudodifferential operators
 LittlewoodPaley theory
 The action of pseudodifferential operators on Sobolev spaces
 Appendix A. Some useful results on the Heisenberg group
 Appendix B. WeylHörmander symbolic calculus on the Heisenberg group
 Bibliography
