Bounded H_\infty-calculus for pseudodifferential Douglis-Nirenberg systems of mild regularity

We consider pseudodifferential Douglis-Nirenberg systems on \rz^n with components belonging to the standard Hörmander class S^*_{1,\delta}(\rz^n\times\rz^n), 0\le\delta<1. Parameter-ellipticity with respect to a subsector \Lambda\subset\cz is introduced and shown to imply the existence of a bounded H_\infty-calculus in suitable scales of Sobolev, Besov, and Hölder spaces. We also admit non pseudodifferential perturbations. Applications concern systems with coefficients of mild Hölder regularity and the generalized thermoelastic plate equations.