A pseudo-differential calculus on the Heisenberg group

Abstract

In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We particularise to this group our general construction [4,3,2] of pseudo-differential calculi on graded groups. The relation between the Weyl quantization and the representations of the Heisenberg group enables us to consider here scalar-valued symbols. We find that the conditions defining the symbol classes are similar but different to the ones in [1]. Applications are given to Schwartz hypoellipticity and to subelliptic estimates on the Heisenberg group.

9 pages

References in corpus (2)

• A pseudo-differential calculus on graded Lie groups
• Lower bounds for operators on graded Lie groups

Cited by in corpus (4)

• Twisted Pseudo-differential Operators on Type I Locally Compact Groups
• Quantizations on Nilpotent Lie Groups and Algebras Having Flat Coadjoint Orbits
• Analytic functional calculus and Gårding inequality on graded Lie groups with applications to diffusion equations
• Global and Concrete Quantizations on General Type I Groups