A Landau-Kolmogorov inequality for Orlicz spaces (Q1870928)
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scientific article; zbMATH DE number 1910306
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Landau-Kolmogorov inequality for Orlicz spaces |
scientific article; zbMATH DE number 1910306 |
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A Landau-Kolmogorov inequality for Orlicz spaces (English)
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14 May 2003
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It is shown that for the half-line \(\mathbb{R}_+\) and any Young function with corresponding Orlicz norm the Landau inequality \[ \|f^{(k)}\|^n\leq K(k, n)\|f\|^{n- k}\|f^{(n)}\|^k,\quad 0< k< n, \] holds with optimal \(K(k,n)=\) the \(K\) for the \(L^\infty\)-norm on \(\mathbb{R}_+\); the same holds for any Luxemburg norm.
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Landau-Kolmogorov inequality
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Orlicz norm
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Luxemburg norm
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