  We consider two kinds of higher dimensional models which upon dimensional
reduction lead to Jordan-Brans-Dicke type effective actions in four dimensions
with the scale factor of the extra dimensions playing the role of the JBD
field. These models are characterized by the potential for the JBD field which
arises from the process of dimensional reduction, and by the coupling of the
inflaton sector with the JBD field in the Jordan frame. Taking into account the
fact that these models allow the possibility of enough inflation and dynamical
compactification of the extra dimensions, we examine in the context of these
models the other conditions which need to be satisfied for a viable scenario of
extended inflation. We find that the requirements of conforming to general
relativity at the present epoch, and producing suitable bubble spectrums during
inflation lead to constraints on the allowed values taken by the parameters of
these models. A model with a ten dimensional JBD field is able to satisfy the
condition for appropriate density perturbations viewed in the conformal
Einstein frame, with a stringent restriction on the initial value taken by the
scale factor of the extra dimensions.
