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.
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Korytov, I.V. Clarkson’s inequalities for periodic Sobolev space. Lobachevskii J Math 38, 1146–1155 (2017). https://doi.org/10.1134/S1995080217060178
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DOI: https://doi.org/10.1134/S1995080217060178