After introducing the notion and the significance of a bounded H∞-calculus for linear operators we will prove that the Stokes operator on Lqσ(Ω) admits this property.
Here Ω is a domain in Rn either bounded, exterior, or a perturbed half-space.
The starting point will be the result on the half-space. By using an abstract perturbation theorem, this result can be transfered to bent half-spaces.
The application of a localizaton procedure then will lead to the bounded H∞-calculus for the Stokes operator on Lqσ(Ω) for the mentioned domains Ω.