TY - JOUR
T1 - A pseudo-differential calculus on the Heisenberg group
AU - Fischer, Veronique
AU - Ruzhansky, Michael
PY - 2014/3
Y1 - 2014/3
N2 - 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 [1]. Applications are given to Schwartz hypoellipticity and to subelliptic estimates on the Heisenberg group.
AB - 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 [1]. Applications are given to Schwartz hypoellipticity and to subelliptic estimates on the Heisenberg group.
UR - http://dx.doi.org/10.1016/j.crma.2013.12.006
UR - https://www.scopus.com/pages/publications/84894261115
U2 - 10.1016/j.crma.2013.12.006
DO - 10.1016/j.crma.2013.12.006
M3 - Article
SN - 1631-073X
VL - 352
SP - 197
EP - 204
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 3
ER -