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This article is cited in 24 scientific papers (total in 24 papers)
The Hardy–Littlewood–Pólya inequality for analytic functions in Hardy–Sobolev spaces
K. Yu. Osipenko Moscow State Aviation Technological University
Abstract:
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.
Received: 29.03.2005 and 05.08.2005
Citation:
K. Yu. Osipenko, “The Hardy–Littlewood–Pólya inequality for analytic functions in Hardy–Sobolev spaces”, Sb. Math., 197:3 (2006), 315–334
Linking options:
https://www.mathnet.ru/eng/sm1537https://doi.org/10.1070/SM2006v197n03ABEH003760 https://www.mathnet.ru/eng/sm/v197/i3/p15
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Abstract page: | 972 | Russian version PDF: | 458 | English version PDF: | 20 | References: | 81 | First page: | 1 |
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