Smoothness and function spaces generated by homogeneous multipliers (Q416332)
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scientific article; zbMATH DE number 6032367
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Smoothness and function spaces generated by homogeneous multipliers |
scientific article; zbMATH DE number 6032367 |
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Smoothness and function spaces generated by homogeneous multipliers (English)
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10 May 2012
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Summary: Differential operators generated by homogeneous functions \(\psi\) of an arbitrary real order \(s > 0 ~(\psi\)-derivatives) and related spaces of \(s\)-smooth periodic functions of \(d\) variables are introduced and systematically studied. The obtained scale is compared with the scales of Besov and Triebel-Lizorkin spaces. Explicit representation formulas for \(\psi\)-derivatives are obtained in terms of the Fourier transform of their generators. Some applications to approximation theory are discussed.
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Besov spaces
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Triebel-Lizorkin spaces
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