  We prove the existence and uniqueness of a projectively equivariant symbol
map (in the sense of Lecomte and Ovsienko) for the spaces $D_p$ of differential
operators transforming p-forms into functions. These results hold over a smooth
manifold endowed with a flat projective structure.
  As an application, we classify the Vect(M)-equivariant maps from $D_p$ to
$D_q$ over any manifold M, recovering and improving earlier results by N.
Poncin. This provides the complete answer to a question raised by P. Lecomte
about the extension of a certain intrinsic homotopy operator.
