Direct and reverse Carleson measures for $\mathcal{H}(b)$ spaces

TL;DR

This paper investigates the properties of direct and reverse Carleson measures within de Branges-Rovnyak spaces, focusing on cases where the function b is a non-extreme point of the unit ball in H-infinity, providing new insights into measure characterizations.

Contribution

It offers new characterizations of Carleson measures for  spaces when b is a non-extreme point, extending previous understanding of these measures.

Findings

Characterization of Carleson measures for  spaces.

Analysis of measures when b is a non-extreme point.

Extension of measure theory in de Branges-Rovnyak spaces.

Abstract

In this paper we discuss direct and reverse Carleson measures for the de Branges-Rovnyak spaces $\mathcal{H}(b)$, mainly when b is a non-extreme point of the unit ball of $H^{\infty}$.