Asymptotic expansions for Hormander symbol classes in the calculus of pseudo-differential operators

We establish formulas for asymptotic expansions for S(m, g), the Hormander class parameterized by the metric g and weight function m, defined on the phase space. By choosing m and g in appropriate ways, we cover some classical results on expansions for symbol classes of the form S-rho,delta(tau), and by choosing m and g in other ways we obtain asymptotic expansions for (generalized) SG classes.