  By appeal to Distribution Theory we discuss in rigorous fashion, without
appealing to {\bf any conjecture} (as usually done by other authors), the
boundary-bulk propagators for the scalar field, both in the non-massive and
massive cases. These calculations, new in the literature as far as we know, are
carried out in two instances: (i) when the boundary is a Euclidean space and
(ii) when it is of Minkowskian nature. In this last case we compute also three
propagators: Feynman's, Anti-Feynman's, and Wheeler's (half advanced plus half
retarded). For an operator corresponding to scalar field we obtain the two
points correlations functions in the three instances above mentioned
