Let (M,ω) be a symplectic foliation with a symplectic form. Let A be an Heisenberg pseudodifferential operator. In this paper, we define the noncommutative residue of A for the symplectic foliation, using a symplectic form. Moreover, we show that is the unique trace on the algebra of Heisenberg pseudodifferential operators up to multiplication by a constant and we related it to the Dixmier trace in the given space.
2020 Mathematics Subject Classification : 58J42; 58B34; 58J40.