  We establish resolvent estimates in spaces of bounded solenoidal functions
for the Stokes operator in a bounded domain $\Omega$ in $R^d$ under the
assumptions that $\Omega$ is $C^1$ for $d\ge 3$ and Lipschitz for $d=2$. As a
corollary, it follows that the Stokes operator generates a uniformly bounded
analytic semigroup in the spaces of bounded solenoidal functions in $\Omega$.
The smoothness conditions on $\Omega$ are sharp. The case of exterior domains
with nonsmooth boundaries is also studied.The key step in the proof involves
new estimates which connect the pressure to the velocity in the $L^q$ average,
but only on scales above certain level.
