Clarkson’s inequalities for periodic Sobolev space
- Авторлар: Korytov I.1
-
Мекемелер:
- National Research Tomsk Polytechnic University
- Шығарылым: Том 38, № 6 (2017)
- Беттер: 1146-1155
- Бөлім: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/200672
- DOI: https://doi.org/10.1134/S1995080217060178
- ID: 200672
Дәйексөз келтіру
Аннотация
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.
Авторлар туралы
I. Korytov
National Research Tomsk Polytechnic University
Хат алмасуға жауапты Автор.
Email: korytov@tpu.ru
Ресей, Tomsk, 634050