  In this paper we give a solution formula for the two-phase Stokes equations
with and without surface tension and gravity in the whole space with flat
interface. The solution formula has already considered by Shibata-Shimizu.
However we reconstruct the formula so that we are able to prove resolvent
estimate and maximal regularity estimate. In the previous work, they needed to
assume additional conditions on normal components. We also take care of normal
components, while the assumption becomes weaker than before. The method is
based on an $H^\infty$ calculus which has already used for the Stokes problems
with various boundary conditions in the half space.
