Bounded H∞‐calculus for pseudo‐differential Douglis–Nirenberg systems of mild regularity
Robert Denk, Jürgen Saal, Jörg Seiler · Mathematische Nachrichten · 2009
Abstract We consider pseudo‐differential Douglis–Nirenberg systems on ℝn with components belonging to the standard Hörmander class S1,δ *(ℝn × Rn ), 0 ≤ δ < 1. Parameter‐ellipticity with respect to a subsector Λ ⊂ ℂ is introduced and shown to imply the existence of a bounded H∞‐calculus in suitable scales of Sobolev, Besov, and Hölder spaces. We also admit non pseudo‐differential perturbations. Applications concern systems with coefficients of mild Hölder regularity and the generalized thermoelastic plate equations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)