We consider the Sp(2n) invariant formulation of higher spin fields on
flat and curved backgrounds of constant curvature.  In this formulation
an infinite number of higher spin fields are packed into single scalar
and spinor master fields (hyperfields) propagating on extended spaces,
to be called hyperspaces, parametrized by tensorial coordinates. We show
that the free field equations on flat and AdS--like hyperspaces are
related to each other by a generalized conformal transformation of the
scalar and spinor master fields and show how to compute Green functions.