  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. We compute the
four--point functions on a flat hyperspace for both scalar and spinor master
fields, thus extending the two-- and three--point function results of
arXiv:hep-th/0312244. Then using the generalized conformal transformation we
derive two--, three-- and four--point functions on AdS--like hyperspace from
the corresponding correlators on the flat hyperspace.
