Carleson measures, multipliers and integration operators for spaces of Dirichlet type

For 0<p<∞ and α>−1, 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 D such that , 0<p<q<∞. We also characterize the pointwise multipliers from to (0<p<q<∞) if p−2<α<p. In particular, we prove that if the only pointwise multiplier from to (0<p<q<∞) 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.