Bounded H∞-calculus for pseudodifferential Douglis-Nirenberg systems of mild regularity
R. Denk, J. Saal, J. Seiler
Abstract. We consider pseudo-differential Douglis–Nirenberg systems on Rn with components belonging to the standard Hörmander class. Parameter-ellipticity with respect to a subsector of the complex plane 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.
Math. Nachr. 282 (2009), 386-407.
The paper is available here: Preprint version