In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We particularise to this group our general construction [4,2,3] of pseudo-differential calculi on graded groups. The relation between the Weyl quantisation 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 . Applications are given to Schwartz hypoellipticity and to subelliptic estimates on the Heisenberg group. © 2014 Académie des sciences.
Fischer, V., & Ruzhansky, M. (2014). A pseudo-differential calculus on the Heisenberg group. Comptes Rendus Mathematique, 352(3), 197–204. https://doi.org/10.1016/j.crma.2013.12.006