Abstract. We investigate Carleson measures $\mu $ on $\overline{\msbm D}$ where ${\msbm D}$ is the open unit disk in ${\msbm C}$, along with functional analytic properties of the formal identity of the Hardy space $H^p({\msbm D})$ into the Lebesgue space $L^q(\mu )$, for any previously fixed $0< p,q< \infty $. Our corresponding characterizations do not only extend the classical results for measures concentrated on ${\msbm D}$ 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.

AMS Subject Classification (1991): 47B38, 46E5, 30D55, 47B33

Keyword(s): Carleson measures, Carleson embeddings, Hardy spaces, compactness properties

Received April 8, 2004. (Registered under 5875/2009.)