Reverse Carleson measures in Hardy spaces

Abstract

We give a necessary and sufficient condition for a measure $\mu$ in the closed unit disk to be a reverse Carleson measure for Hardy spaces. This extends a previous result of Lefèvre, Li, Queffélec and Rodríguez-Piazza Lefèvre et al. (Rev Mat Iberoam 28(1):57-76, 2012). We also provide a simple example showing that the analogue for the Paley-Wiener space does not hold. As it turns out the analogue never holds in any model space.