  As an extension of the so-called BMN conjecture, we investigate the
plane-wave limit for possible holographic connection between bulk string
theories in non-conformal backgrounds of D$p$-branes and the corresponding
supersymmetric gauge theories for $p<5$. Our work is based on the tunneling
picture for dominant null trajectories of strings in the limit of large angular
momentum. The tunneling null trajectories start from the near-horizon boundary
and return to the boundary, and the resulting backgrounds are time-dependent
for general D$p$-branes except for $p=3$. We develop a general method for
extracting diagonalized two-point functions for boundary theories as Euclidean
(bulk) S-matrix in the time-dependent backgrounds. For the case of D0-brane,
two-point functions of supergravity modes are shown to agree with the results
derived previously by the perturbative analysis of supergravity. We then
discuss the implications of the holography for general cases of D$p$-branes
including the stringy excitations. All the cases ($p\ne 3, p<5$) exhibit
interesting infra-red behaviors, which are different from free-field theories,
suggesting the existence of quite nontrivial fixed-points in dual gauge
theories.
