Reverse Carleson embeddings for model spaces

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‖L2(μ) ≤ c‖f‖H2 for all f ∈ H, the Hardy space of the unit disk. Lefèvre et al. examined measures μ for which there exists a positive constant c such that ‖f‖L2(μ) ≥ c‖f‖H2 for all f ∈ H. The first type of inequality above was explored with H replaced by one of the model spaces (ΘH2)⊥ by Aleksandrov, Baranov, Cohn, Treil, and Volberg. In this paper we discuss the second type of inequality in (ΘH2)⊥.