  We analyze the propagation of a scalar field in multidimensional theories
which include kinetic corrections in the brane, as a prototype for
gravitational interactions in a four dimensional brane located in a (nearly)
flat extra dimensional bulk. We regularize the theory by introducing an
infrared cutoff given by the size of the extra dimensions and a physical
ultraviolet cutoff of the order of the fundamental Planck scale in the higher
dimensional theory. We show that, contrary to recent suggestions, the radius of
the extra dimensions cannot be arbitrarily large. Moreover, for finite radii,
the gravitational effects localized on the brane can substantially alter the
phenomenology of collider and/or table-top gravitational experiments. This
phenomenology is dictated by the presence of a massless graviton, with standard
couplings to the matter fields, and a massive graviton which couples to matter
in a much stronger way. While graviton KK modes lighter than the massive
graviton couple to matter in a standard way, the couplings to matter of the
heavier KK modes are strongly suppressed.
