Geodesic
Weakly Outer Inner Functions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 2, pp. 7-15

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An inner function $I$ in the unit ball $B_n\subset\mathbb{РЎ}^n$ is said to be weakly outer if the closed subspace $IH^p(B_n)$ is weakly dense in the Hardy space $H^p(B_n)$, $0$. We construct weakly outer inner functions in the ball $B_n$ for all $n\ge 1$. We also investigate inner functions $I$ such that the subspace $I H^p(B_n)$ is not weakly dense in $H^p(B_n)$.
Keywords: Hardy class, pluriharmonic measure. 
@article{FAA_2003_37_2_a1,
     author = {E. Doubtsov},
     title = {Weakly {Outer} {Inner} {Functions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {7--15},
     publisher = {mathdoc},
     volume = {37},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2003_37_2_a1/}
}
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E. Doubtsov. Weakly Outer Inner Functions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 37 (2003) no. 2, pp. 7-15. http://geodesic.mathdoc.fr/item/FAA_2003_37_2_a1/