The Bellman function, the two-weight Hilbert transform, and embeddings of the model spacesKθ

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Symbols of truncated Toeplitz operators (2010, background): “ntinuability) of the elements of Kp θ on the boundary. The problem of the description of the class Dp(θ) for general θwas posed by Cohn in 1982; it is still open. Many partial results may be found in [18, 19, 33, 6, 26, 7, 8]. In particular, the classes Dp(θ) are described if θis a one-component inn”
Bounded symbols and Reproducing Kernel Thesis for truncated Toeplitz operators (2009, background): “µbe a positive measure on T such that the singular part of µis supported on a subset of T \σ(Θ); is it suﬃcient to have sup λ∈D Z T |hΘ λ| 2 dµ<+∞, to deduce that µis a Carleson measure for KΘ? In [23] Nazarov and Volberg construct a counterexample to this question with a measure µof the form dµ=”
Bernstein-type inequalities for shift-coinvariant subspaces and their applications to Carleson embeddings (2005, background): “As in the Volberg–Treil theorem we consider the measures with Carleson-type estimate on a special class of sufficiently large squares.”