  The vacuum expectation value of the square of the field fluctuations of a
scalar field on a background consisting of {\it two} de Sitter branes embedded
in an anti-de Sitter bulk are considered. We apply a dimensional reduction to
obtain an effective lower dimensional de Sitter space equation of motion with
associated Kaluza-Klein masses and canonical commutation relations. The case of
a scalar field obeying a restricted class of mass and curvature couplings,
including massless, conformal coupling as a special case, is considered. We
find that the local behaviour of the quantum fluctuations suffers from surface
divergences as we approach the brane, however, if the field is {\it
constrained} to its value on the brane from the beginning then surface
divergences disappear. The ratio of $<\phi^2>$ between the Kaluza-Klein
spectrum and the lowest eigenvalue mode is found to vanish in the limit that
one of the branes goes to infinity.
