Geodesic
The Hardy–Littlewood–Pólya inequality for analytic functions in Hardy–Sobolev spaces
Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 315-334 
K. Yu. Osipenko. The Hardy–Littlewood–Pólya inequality for analytic functions in Hardy–Sobolev spaces. Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 315-334. http://geodesic.mathdoc.fr/item/SM_2006_197_3_a1/
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     author = {K. Yu. Osipenko},
     title = {The {Hardy{\textendash}Littlewood{\textendash}P\'olya} inequality for analytic functions in {Hardy{\textendash}Sobolev} spaces},
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     volume = {197},
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     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_3_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a function of a complex variable analytic in a strip the extremum of the $L_2(\mathbb R)$ norm of the $k$th derivative is found under a constraint on the $L_2(\mathbb R)$-norm of the function and the norm of its $n$th derivative in the metric of the Hardy–Sobolev space. The closely connected problem of the optimal recovery of the $k$th derivative of a function in the Hardy–Sobolev class from the inaccurately given trace of this function on the real axis is also studied. An optimal recovery method is found. Bibliography: 10 titles.

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[9] G. G. Magaril-Ilyaev, K. Yu. Osipenko, “Optimalnoe vosstanovlenie funktsii i ikh proizvodnykh po koeffitsientam Fure, zadannym s pogreshnostyu”, Matem. sb., 193:3 (2002), 79–100 | MR | Zbl

[10] G. G. Magaril-Ilyaev, K. Yu. Osipenko, “Optimalnoe vosstanovlenie funktsii i ikh proizvodnykh po priblizhennoi informatsii o spektre i neravenstva dlya proizvodnykh”, Funkts. analiz i ego prilozh., 37:3 (2003), 51–64 | MR | Zbl