  We determine the boundedness and compactness of a large class of operators,
mapping from general Banach spaces of holomorphic functions into a particular
type of spaces of functions determined by the growth of the functions, or the
growth of the functions derivatives. The results show that the boundedness and
compactness of such intrinsic operators depends only on the behaviour on the
point evaluation functionals. They also generalize previous similar results
about several specific classes of operators, such as the multiplication,
composition and integral operators.
