Geodesic
Admissibility criteria for model subspaces with fast growth of the argument of the generating inner function
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 35, Tome 345 (2007), pp. 55-84

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Let $\Theta$ be an inner function in the upper half plane and let $K_\Theta=H^2\ominus\Theta H^2$ be the associated model subspace of the Hardy space $H^2$. We call a non-negative function $\omega$ $\Theta$-admissible if in the space $K_\Theta$ there exists a non-zero function $f\in K_\Theta$ such that $|f|\leq\omega$ a.e. on $\mathbb{R}$. We give some sufficient conditions of $\Theta$-admissibility for the case when $\Theta$ is meromorphic and $\arg\Theta$ grows fast ($(\arg\Theta)'$ tends to infinity). 
@article{ZNSL_2007_345_a3,
     author = {Yu. S. Belov},
     title = {Admissibility criteria for model subspaces with fast growth of the argument of the generating inner function},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {55--84},
     publisher = {mathdoc},
     volume = {345},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_345_a3/}
}
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Yu. S. Belov. Admissibility criteria for model subspaces with fast growth of the argument of the generating inner function. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 35, Tome 345 (2007), pp. 55-84. http://geodesic.mathdoc.fr/item/ZNSL_2007_345_a3/