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 ZeitschriftenZeitschriftenaufsätzeForschungbegutachtet

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@article{aa351bcf8919457ab63f1adcba4cb276,
title = "Wavelet characterizations for anisotropic Besov spaces",
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.",
keywords = "Mathematics, wavelets, anisotropic function spaces, Besov spaces, approximation spaces, Jackson estimates, interpolation, embedding",
author = "Reinhard Hochmuth",
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 Universit{\"a}t Gesamthochschule Kassel.",
year = "2002",
month = mar,
day = "1",
doi = "10.1006/acha.2001.0377",
language = "English",
volume = "12",
pages = "179--208",
journal = "Applied and Computational Harmonic Analysis",
issn = "1063-5203",
publisher = "Elsevier B.V.",
number = "2",

}

RIS

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 -

DOI