Wavelet characterizations for anisotropic Besov spaces
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Wavelet characterizations for anisotropic Besov spaces. / Hochmuth, Reinhard.
in: Applied and Computational Harmonic Analysis, Jahrgang 12, Nr. 2, 01.03.2002, S. 179-208.Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › begutachtet
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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 - 2002/3/1
Y1 - 2002/3/1
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 L p-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 L p-spaces with 0 < p < ∞ are derived.
KW - Mathematics
KW - wavelets
KW - anisotropic function spaces
KW - Besov spaces
KW - approximation spaces
KW - Jackson estimates
KW - interpolation
KW - embedding
UR - http://www.scopus.com/inward/record.url?scp=0010993756&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/10c0c630-4a86-3ae4-9c07-358233dd08ec/
U2 - 10.1006/acha.2001.0377
DO - 10.1006/acha.2001.0377
M3 - Journal articles
VL - 12
SP - 179
EP - 208
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
SN - 1063-5203
IS - 2
ER -