  We study in detail the extension of the generalized conformal symmetry
proposed previously for D-particles to the case of supersymmetric Yang-Mills
matrix models of Dp-branes for arbitrary p. It is demonstrated that such a
symmetry indeed exists both in the Yang-Mills theory and in the corresponding
supergravity backgrounds produced by Dp-branes. On the Yang-Mills side, we
derive the field-dependent special conformal transformations for the collective
coordinates of Dp-branes in the one-loop approximation, and show that they
coincide with the transformations on the supergravity side. These
transformations are powerful in restricting the forms of the effective actions
of probe D-branes in the fixed backgrounds of source D-branes. Furthermore, our
formalism enables us to extend the concept of (generalized) conformal symmetry
to arbitrary configurations of D-branes, which can still be used to restrict
the dynamics of D-branes. For such general configurations, however, it cannot
be endowed a simple classical space-time interpretation at least in the static
gauge adopted in the present formulation of D-branes.
