Details
| Original language | English |
|---|---|
| Pages (from-to) | 179-208 |
| Number of pages | 30 |
| Journal | Applied and Computational Harmonic Analysis |
| Volume | 12 |
| Issue number | 2 |
| Publication status | Published - Mar 2002 |
| Externally published | Yes |
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 Lp-spaces with 0 < p < ∞ are derived.
Keywords
- Anisotropic function spaces, Approximation spaces, Besov spaces, Embedding, Interpolation, Jackson estimates, Wavelets
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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In: Applied and Computational Harmonic Analysis, Vol. 12, No. 2, 03.2002, p. 179-208.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Wavelet characterizations for anisotropic Besov spaces
AU - Hochmuth, Reinhard
N1 - 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.
PY - 2002/3
Y1 - 2002/3
N2 - 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 Lp-spaces with 0 < p < ∞ are derived.
AB - 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 Lp-spaces with 0 < p < ∞ are derived.
KW - Anisotropic function spaces
KW - Approximation spaces
KW - Besov spaces
KW - Embedding
KW - Interpolation
KW - Jackson estimates
KW - Wavelets
UR - http://www.scopus.com/inward/record.url?scp=0010993756&partnerID=8YFLogxK
U2 - 10.1006/acha.2001.0377
DO - 10.1006/acha.2001.0377
M3 - Article
AN - SCOPUS:0010993756
VL - 12
SP - 179
EP - 208
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
SN - 1063-5203
IS - 2
ER -