Carleson-type embeddings with closed range

Abstract

We characterize the Carleson measures $\hat{I}¼$ on the unit disk for which the image of the Hardy space $H^p$ under the corresponding embedding operator is closed in $L^p(\hat{I}¼)$. In fact, a more general result involving $(p,q)$-Carleson measures is obtained. A similar problem is solved in the setting of Bergman spaces.

13 pages