Clarkson’s inequalities for periodic Sobolev space; Lobachevskii Journal of Mathematics; Vol. 38, iss. 6

Clarkson’s inequalities for periodic Sobolev space; Lobachevskii Journal of Mathematics; Vol. 38, iss. 6

Bibliographic Details
Parent link:Lobachevskii Journal of Mathematics.— , 1998-
Vol. 38, iss. 6.— 2017.— [P. 1146–1155]
Main Author: Korytov I. V. Igor Vitalievich
Corporate Author: Национальный исследовательский Томский политехнический университет (ТПУ) Физико-технический институт (ФТИ) Кафедра высшей математики и математической физики (ВММФ)
Summary:Title screen
The validity of Clarkson’s inequalities for periodic functions in the Sobolev space normed without the use of pseudodifferential operators is proved. The norm of a function is defined by using integrals over a fundamental domain of the function and its generalized partial derivatives of all intermediate orders. It is preliminarily shown that Clarkson’s inequalities hold for periodic functions integrable to some power p over a cube of unit measure with identified opposite faces. The work is motivated by the necessity of developing foundations for the functional-analytic approach to evaluating approximation methods.
Режим доступа: по договору с организацией-держателем ресурса
Language:English
Published: 2017
Subjects:
электронный ресурс
труды учёных ТПУ
равномерные выпуклости
единичные сферы
банахово пространство
пространство Соболева
гильбертово пространство
функциональное пространство
обратное неравенство Минковского
неравенства Кларксона
uniform convexity of the unit sphere
Banach space
Sobolev space
non-Hilbert space
periodic function space
inverse Minkowski inequality
cube of unit measure
Clarksons inequalities
Online Access:https://doi.org/10.1134/S1995080217060178
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=657462

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