Phase-space analysis and pseudodifferential calculus on the Heisenberg group

Abstract

This paper has been withdrawn by the authors. 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.

This paper has been withdrawn by the authors. Please see arXiv:1005.0833

References in corpus (1)

• Hörmander type pseudodifferential calculus on homogeneous groups

Cited by in corpus (7)

• A pseudo-differential calculus on the Heisenberg group
• Lower bounds for operators on graded Lie groups
• Pseudo-differential operators associated to general type I locally compact groups
• On $L^2$-boundedness of pseudo-multipliers associated to the Grushin operator
• Calculus of Operators: Covariant Transform and Relative Convolutions
• Global and Concrete Quantizations on General Type I Groups
• Symbolic calculus and convolution semigroups of measures on the Heisenberg group