Smoothness and Function Spaces Generated by Homogeneous Multipliers
Differential operators generated by homogeneous functions ψ of an arbitrary real order s>0 (ψ-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 space...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/643135 |
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| Summary: | Differential operators generated by homogeneous functions ψ of an arbitrary real order s>0 (ψ-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 ψ-derivatives are obtained in terms of the Fourier transform of their generators. Some applications to approximation theory are discussed. |
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| ISSN: | 0972-6802 1758-4965 |