The Hardy-Littlewood-Pólya inequality for analytic functions in Hardy-Sobolev spacesстатья
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Дата последнего поиска статьи во внешних источниках: 19 июня 2014 г.
Аннотация: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.