Geodesic
The Hardy--Littlewood--P\'olya inequality for analytic functions in Hardy--Sobolev spaces
Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 315-334

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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     author = {K. Yu. Osipenko},
     title = {The {Hardy--Littlewood--P\'olya} inequality for analytic functions in {Hardy--Sobolev} spaces},
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K. Yu. Osipenko. The Hardy--Littlewood--P\'olya 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/