Geodesic
Inner functions and spaces of pseudocontinuable functions related to them
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 17, Tome 170 (1989), pp. 7-33

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Let $\theta$ be an inner function; $\alpha\in\mathbb{C}$, $|\alpha|=1$. Then the harmonic function $\mathop{\mathrm{Re}}\frac{\alpha+\theta}{\alpha-\theta}$ is the Poisson integral of a singular measure $\sigma_\alpha$. The Clark theorem allows naturally to identify $H^2\ominus\theta H^2$ with $L^2(\sigma_\alpha)$. The aim of this paper is to investigate $L^p$-properties of this identification operator for $p\ne2$. 
@article{ZNSL_1989_170_a1,
     author = {A. B. Aleksandrov},
     title = {Inner functions and spaces of pseudocontinuable functions related to them},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--33},
     publisher = {mathdoc},
     volume = {170},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_170_a1/}
}
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A. B. Aleksandrov. Inner functions and spaces of pseudocontinuable functions related to them. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 17, Tome 170 (1989), pp. 7-33. http://geodesic.mathdoc.fr/item/ZNSL_1989_170_a1/