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