Reverse Carleson measures in Hardy spaces

TL;DR

This paper characterizes reverse Carleson measures for Hardy spaces, extending previous results, and demonstrates that similar properties do not hold for Paley-Wiener spaces, with implications for model spaces.

Contribution

It provides a necessary and sufficient condition for reverse Carleson measures in Hardy spaces, extending prior work and exploring limitations in related function spaces.

Findings

Characterization of reverse Carleson measures for Hardy spaces

Counterexample showing the analogue fails in Paley-Wiener space

Extension to model spaces associated with one-component inner functions

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 Lef\'evre, Li, Queff\'elec and Rodr\'{\i}guez-Piazza \cite{LLQR}. We also provide a simple example showing that the analogue for the Paley-Wiener space does not hold. This example can be generalised to model spaces associated to one-component inner functions.