  We prove resolvent $L_p$ estimates and maximal $L_p$-$L_q$ regularity
estimates for the Stokes equations with Dirichlet, Neumann and Robin boundary
conditions in the half space. Each solution is constructed by a Fourier
multiplier of $x'$-direction and an integral of $x_N$-direction. We decompose
the solution such that the symbols of the Fourier multipliers are bounded and
holomorphic. We see that the operator norms are dominated by a homogeneous
function of order $-1$ for $x_N$-direction. The basis are Weis's
operator-valued Fourier multiplier theorem and a boundedness of a kernel
operator. We give a new simple approach to get maximal regularity in the half
space.
