Wavelet characterizations for anisotropic Besov spaces

Reinhard Hochmuth

doi:10.1006/acha.2001.0377

Wavelet characterizations for anisotropic Besov spaces

Reinhard Hochmuth

Universität Kassel

Publikation: Beiträge in Zeitschriften › Zeitschriftenaufsätze › Forschung › Begutachtung

45 Zitate (Scopus)

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.

Originalsprache	Englisch
Zeitschrift	Applied and Computational Harmonic Analysis
Jahrgang	12
Ausgabenummer	2
Seiten (von - bis)	179-208
Seitenumfang	30
ISSN	1063-5203
DOIs	https://doi.org/10.1006/acha.2001.0377
Publikationsstatus	Erschienen - 01.03.2002
Extern publiziert	Ja

Bibliographische Notiz

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.

Fachgebiete und Schlagwörter

Mathematik

ASJC Scopus Sachgebiete

Angewandte Mathematik

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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.",

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author = "Reinhard Hochmuth",

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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.

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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 - https://www.scopus.com/pages/publications/0010993756

UR - https://www.mendeley.com/catalogue/10c0c630-4a86-3ae4-9c07-358233dd08ec/

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DO - 10.1006/acha.2001.0377

M3 - Journal articles

SN - 1063-5203

VL - 12

SP - 179

EP - 208

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

IS - 2

ER -

Wavelet characterizations for anisotropic Besov spaces

Abstract

Bibliographische Notiz

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