Geodesic
Embeddings of model subspaces of the Hardy space: compactness
Izvestiya. Mathematics , Tome 73 (2009) no. 6, pp. 1077-1100

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We study properties of the embedding operators of model subspaces $K^p_{\Theta}$ (defined by inner functions) in the Hardy space $H^p$ (coinvariant subspaces of the shift operator). We find a criterion for the embedding of $K^p_{\Theta}$ in $L^p(\mu)$ to be compact similar to the Volberg–Treil theorem on bounded embeddings, and give a positive answer to a question of Cima and Matheson. The proof is based on Bernstein-type inequalities for functions in $K^p_{\Theta}$. We investigate measures $\mu$ such that the embedding operator belongs to some Schatten–von Neumann ideal.
Keywords: Hardy space, inner function, embedding theorem, Carleson measure. 
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     author = {A. D. Baranov},
     title = {Embeddings of model subspaces of the {Hardy} space: compactness},
     journal = {Izvestiya. Mathematics },
     pages = {1077--1100},
     publisher = {mathdoc},
     volume = {73},
     number = {6},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2009_73_6_a0/}
}
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A. D. Baranov. Embeddings of model subspaces of the Hardy space: compactness. Izvestiya. Mathematics , Tome 73 (2009) no. 6, pp. 1077-1100. http://geodesic.mathdoc.fr/item/IM2_2009_73_6_a0/