Abstract
We investigate Carleson measures µ on D where D is the open unit disk in C, along with functional analytic properties of the formal identitiy of the Hardy space H p (D) into the Lebesgue space Lq (µ), for any previously fixed 0 < p, q <
∞. Our corresponding characterizations do not only extend the classical results for measures concentrated on D but also provide different proofs for the latter ones. Among the
applications are generalizations to formal identities as above of several results which have been known for composition operators only.
La Blasco Cruz, O