Invariant pseudodifferential operators on two step nilpotent Lie groups. II (Q1113393)

[For part I see ibid. 29, 315-328 (1982; Zbl 0524.35102).] In a previous paper by the author [Trans. Am. Math. Soc. 280, 721-736 (1983; Zbl 0545.35098)] a method was given for constructing parametrices and inverses for invariant hypoelliptic pseudodifferential operators which are homogeneous with respect to the natural dilations on a step two nilpotent Lie group. The construction made use of a calculus for invariant pseudodifferential operators described in part I. It is shown here that a similar calculus is also valid in the case of arbitrary dilations on a step two group. The parametrix construction of the above cited paper can then be easily extended to include operators homogeneous with respect to arbitrary dilations. As noted in a paper by the author [Contemp. Math. 27, 231-235 (1984; Zbl 0541.35018)], this construction can be ``microlocalized''.