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

Alain Blandignères (1) , Emmanuel Fricain (2) , Frederic Gaunard (3) , Andreas Hartmann (4) , Willam T. Ross (5)

1 ICJ - Institut Camille Jordan
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 Department of Mathematics
4 IMB - Institut de Mathématiques de Bordeaux
5 Department of Mathematics and Computer Science

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 $H^{\infty}$.

Mots clés: de Branges-Rovnyak spaces; embeddings; Carleson measures; reproducing kernel thesis; (non-)extreme point; corona pairs; Muckenhoupt condition

Domaines: Variables complexes [math.CV]

Alain Blandignères, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann, Willam T. Ross. Direct and reverse Carleson measures for $\mathcal{H}(b)$ spaces. Indiana University Mathematics Journal, 2015, 64 (4), pp.1027-1057. ⟨hal-00850615⟩