For and , we let denote the space of those functions f which are analytic in the unit disc and satisfy . In this paper we characterize the positive Borel measures μ in such that , . We also characterize the pointwise multipliers from to () if . In particular, we prove that if the only pointwise multiplier from to () is the trivial one. This is not longer true for and we give a number of explicit examples of functions which are multipliers from to for this range of values.