Abstract
The goal of this paper is to provide wavelet characterizations for anisotropic Besov spaces. Depending on the anisotropy, appropriate biorthogonal tensor product bases are introduced and Jackson and Bernstein estimates are proved for two-parameter families of finite-dimensional spaces. These estimates lead to characterizations for anisotropic Besov spaces by anisotropy-dependent linear approximation spaces and lead further on to interpolation and embedding results. Finally, wavelet characterizations for anisotropic Besov spaces with respect to L p-spaces with 0 < p < ∞ are derived.
| Original language | English |
|---|---|
| Journal | Applied and Computational Harmonic Analysis |
| Volume | 12 |
| Issue number | 2 |
| Pages (from-to) | 179-208 |
| Number of pages | 30 |
| ISSN | 1063-5203 |
| DOIs | |
| Publication status | Published - 01.03.2002 |
| Externally published | Yes |
Bibliographical note
Funding Information:This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) under Grant Ho 1846/1-1. It was revised and completed while the author held a temporary full position for applied mathematics at the Universität Gesamthochschule Kassel.
Research areas and keywords
- Mathematics
- wavelets
- anisotropic function spaces
- Besov spaces
- approximation spaces
- Jackson estimates
- interpolation
- embedding
ASJC Scopus Subject Areas
- Applied Mathematics
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