Geodesic
An extremal property of outer functions
Matematičeskie zametki, Tome 10 (1971) no. 1, pp. 53-56 
B. I. Korenblum. An extremal property of outer functions. Matematičeskie zametki, Tome 10 (1971) no. 1, pp. 53-56. http://geodesic.mathdoc.fr/item/MZM_1971_10_1_a6/
@article{MZM_1971_10_1_a6,
     author = {B. I. Korenblum},
     title = {An~extremal property of outer functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {53--56},
     year = {1971},
     volume = {10},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_1_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Our main result is the following: if $f(z)$ is in the space $H^2$, and $F(z)$ is its outer part, then $\|F^{(n)}\|_{H^2}\le\|f^{(n)}\|_{H^2}$ $(n=1,2,\dots)$, the left side being finite if the right side is finite. Under certain essential restrictions, this inequality was proved by B.I. Korenblyum and V.S. Korolevich [1].