Boundedness of imaginary powers of the stokes operator in an infinite layer

In this article we prove the existence of bounded purely imaginary powers of the Stokes operator A(q), which is defined on the space of solenoidal vector fields J(q)(Omega), 1 < q < infinity, where Omega = Rn-1 x (-1, 1) is an infinite layer. It is a consequence of a special representation of the resolvent of the Stokes operator in terms of the Stokes operator on R-n, a composition of a trace and a Poisson operator - a singular Green operator - and a negligible part.