On equivalence of moduli of smoothness of splines in \(\mathbb {L}_{p}, 0 < p < 1\) (Q860687)
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scientific article; zbMATH DE number 5083368
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On equivalence of moduli of smoothness of splines in \(\mathbb {L}_{p}, 0 < p < 1\) |
scientific article; zbMATH DE number 5083368 |
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On equivalence of moduli of smoothness of splines in \(\mathbb {L}_{p}, 0 < p < 1\) (English)
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9 January 2007
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The \((k+\nu)\)th modules of smoothness of a spline function in \(L_p\), \(0<p<1\), can be estimated by the \((k+\nu)\)th Ditzian-Totik modulus. The inequality is not valid for arbitrary \(f\in C^\infty\). Here, an inverse inequality is established for the argument \(n^{-1}\).
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modulus of smoothness
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