The Stokes Operator on Exterior Domains in Homogeneous Weighted Function Spaces:From Weak Theory to $\mathscr H^\infty$-calculus to Fractional Domains

We consider the Stokes operator $A$ on smooth exterior domains $Ω$ of $\mathbb{R}^n$ in homogeneous Sobolev spaces $\widehat H^{κ,q}_w(Ω)$ with radially symmetric Muckenhoupt weights $w\in \mathscr A_q$. A fundamental property is the existence of a bounded $\mathscr H^\infty$-calculus of the Stokes