Reverse Carleson Embeddings for Model Spaces

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

1 ICJ - Institut Camille Jordan
2 IMB - Institut de Mathématiques de Bordeaux
3 Department of Mathematics

The classical embedding theorem of Carleson deals with finite positive Borel measures $\mu$ on the closed unit disk for which there exists a positive constant $c$ such that $\|f\|_{L^2(\mu)} \leq c \|f\|_{H^2}$ for all $f \in H^2$, the Hardy space of the unit disk. Lefévre et al.\ examined measures $\mu$ for which there exists a positive constant $c$ such that $\|f\|_{L^2(\mu)} \geq c \|f\|_{H^2}$ for all $f \in H^2$. The first type of inequality above was explored with $H^2$ replaced by one of the model spaces $(\Theta H^2)^{\perp}$ by Aleksandrov, Baranov, Cohn, Treil, and Volberg. In this paper we discuss the second type of inequality in $(\Theta H^2)^{\perp}$.

Mots clés: model spaces; embeddings; dominating sets; Carleson measures; Clark measures

Domaines: Variables complexes [math.CV]

Alain Blandignères, Emmanuel Fricain, Frederic Gaunard, Andreas Hartmann, William T. Ross. Reverse Carleson Embeddings for Model Spaces. Journal of the London Mathematical Society, 2013, 88, pp.437-464. ⟨hal-00697223v2⟩