Clarkson’s inequalities for periodic Sobolev space
- Authors: Korytov I.V.1
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Affiliations:
- National Research Tomsk Polytechnic University
- Issue: Vol 38, No 6 (2017)
- Pages: 1146-1155
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/200672
- DOI: https://doi.org/10.1134/S1995080217060178
- ID: 200672
Cite item
Abstract
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.
About the authors
I. V. Korytov
National Research Tomsk Polytechnic University
Author for correspondence.
Email: korytov@tpu.ru
Russian Federation, Tomsk, 634050