On Embedding Theorems for Coinvariant Subspaces of the Shift Operator. II

By A. Aleksandrov. 2000

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Bounded symbols and Reproducing Kernel Thesis for truncated Toeplitz operators (2009, background): “Remark 7.3. It is shown by Aleksandrov [ 3, Theorem 1.2 ] that the condition”
Symbols of truncated Toeplitz operators (2010, unknown): “4 we need the following obvious lemma (see [5]) based on the relations Kθ2 = Kθ ⊕ θKθ and Kθ ·Kθ ⊂ K 1 θ2 .”
Discrete Hilbert transforms on sparse sequences (2009, background): “Other partial results can be found in [2, 3, 4, 17, 19, 31].”
Hereditary completeness for systems of exponentials and reproducing kernels (2011, background): “Here we give just a result for one-component inner functions E/E (see, for instance, [1]) of special type.”
Bernstein-type inequalities for shift-coinvariant subspaces and their applications to Carleson embeddings (2005, methodology): “We also obtain the estimates relating the weight wp with geometric properties of the level sets of the function (some close results may be found in [5,6]).”