Geodesic
Analytic functions which are regular in a disc and smooth on its boundary
Matematičeskie zametki, Tome 7 (1970) no. 2, pp. 165-172 Cet article a éte moissonné depuis la source Math-Net.Ru

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A theorem is established, asserting that the norm of the derivative $f^{(n)}(z)$ in the space $H^2$ for a function $f(z)$ regular in the disc is not increased if we replace $f$ by the ratio $f(z)/G(z)$, where $G(z)$ is any interior function dividing $f(z)$ whose singular part is of a particular form. 
@article{MZM_1970_7_2_a3,
     author = {B. I. Korenblyum and V. S. Korolevich},
     title = {Analytic functions which are regular in a disc and smooth on its boundary},
     journal = {Matemati\v{c}eskie zametki},
     pages = {165--172},
     year = {1970},
     volume = {7},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_2_a3/}
}
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B. I. Korenblyum; V. S. Korolevich. Analytic functions which are regular in a disc and smooth on its boundary. Matematičeskie zametki, Tome 7 (1970) no. 2, pp. 165-172. http://geodesic.mathdoc.fr/item/MZM_1970_7_2_a3/