Clarkson’s inequalities for periodic Sobolev space; Lobachevskii Journal of Mathematics; Vol. 38, iss. 6
| Источник: | Lobachevskii Journal of Mathematics.— , 1998- Vol. 38, iss. 6.— 2017.— [P. 1146–1155] |
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| Главный автор: | |
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| Примечания: | 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 |
| Язык: | английский |
| Опубликовано: |
2017
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| Online-ссылка: | https://doi.org/10.1134/S1995080217060178 |
| Формат: | Электронный ресурс Статья |
| Запись в KOHA: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=657462 |
| Примечания: | 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 |
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| DOI: | 10.1134/S1995080217060178 |