Geodesic
On the existence of nontangential boundary values of pseudocontinuable functions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 23, Tome 222 (1995), pp. 5-17 
A. B. Aleksandrov. On the existence of nontangential boundary values of pseudocontinuable functions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 23, Tome 222 (1995), pp. 5-17. http://geodesic.mathdoc.fr/item/ZNSL_1995_222_a0/
@article{ZNSL_1995_222_a0,
     author = {A. B. Aleksandrov},
     title = {On the existence of nontangential boundary values of pseudocontinuable functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--17},
     year = {1995},
     volume = {222},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_222_a0/}
}
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Let $\theta$ be an inner functions, let $\theta^*(H^2)=H^2\ominus\theta H^2$, and let $\mu$ be a finite Borel measure on the unit circle $\mathbb T$. Our main purpose is to prove that, if every function $f\in\theta^*(H^2)$ can be defined $\mu$-almost everywhere on $\mathbb T$ in a certain (weak) natural sense, then every function $f\in\theta^*(H^2)$ has finite nontangential boundary values $\mu$-almost everywhere on $\mathbb T$. A similar result is true for the $\mathcal L^p$-analog of $\theta^*(H^2)$ ($p>0$). Bibliography: 17 titles.