Reverse Carleson Embeddings for Model Spaces

Abstract

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 $|f{|}_{L^2(\mu )}\le c|f{|}_{H^2}$ 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 $\Vert f{\Vert }_{L^2(\mu )}\ge c|f{|}_{H^2}$ 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 $(\Theta H^2{)}^{\perp }$.

33 pages

References in corpus (1)

• Compact embeddings of model subspaces of the Hardy space

Cited by in corpus (6)

• Reverse Carleson measures in Hardy spaces
• A survey on reverse Carleson measures
• Rank one perturbations and Anderson-type Hamiltonians
• Carleson-type embeddings with closed range
• Dominant sets for model spaces in several variables
• Direct and reverse Carleson measures for $\mathcal{H}(b)$ spaces