Wavelet characterizations for anisotropic Besov spaces with 0 p 1

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Wavelet characterizations for anisotropic Besov spaces with 0 p 1. / Hochmuth, Reinhard; Garrigós, Gustavo; Tabacco, Anita.
In: Proceedings of the Edinburgh Mathematical Society, Vol. 47, No. 3, 01.10.2004, p. 573-595.

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Hochmuth R, Garrigós G, Tabacco A. Wavelet characterizations for anisotropic Besov spaces with 0 p 1. Proceedings of the Edinburgh Mathematical Society. 2004 Oct 1;47(3):573-595. doi: 10.1017/S001309150300107X

Bibtex

@article{dd696754fac54736bebdd326ae3acc29,
title = "Wavelet characterizations for anisotropic Besov spaces with 0 p 1",
abstract = "We present a wavelet characterization of anisotropic Besov spaces B p,q α(ℝ n), valid for the whole range 0 < p, q < ∞, and in terms of multi-resolution analyses with dilation adapted to the anisotropy of the space. Our proofs combine classical techniques based on Bernstein and Jackson-type inequalities, and nonlinear methods for the cases p < 1. Among the consequences of our results, we characterize B p,q α as a linear approximation space, and derive embeddings and interpolation formulae for B p,q α, which appear to be new in the literature when p < 1. ",
keywords = "Mathematics, Approximation and interpolation spaces, Jackson and Bernstein inequalities, Multilevel decomposition",
author = "Reinhard Hochmuth and Gustavo Garrig{\'o}s and Anita Tabacco",
note = "Funding Information: Acknowledgements. Work partially supported by the European Community Human Potential Programme, contracts HPRN-CT-2002-00286 {\textquoteleft}Breaking Complexity{\textquoteright} and HPRN-CT-2001-00273 {\textquoteleft}HARP{\textquoteright}. G.G. was also supported by {\textquoteleft}Programa Ram{\'o}n y Cajal{\textquoteright} and grant BMF2001-0189, MCyT (Spain). The authors thank an anonymous referee whose careful reading and suggestions led to a much improved version of this paper.",
year = "2004",
month = oct,
day = "1",
doi = "10.1017/S001309150300107X",
language = "English",
volume = "47",
pages = "573--595",
journal = "Proceedings of the Edinburgh Mathematical Society",
issn = "0013-0915",
publisher = "Cambridge University Press",
number = "3",

}

RIS

TY - JOUR

T1 - Wavelet characterizations for anisotropic Besov spaces with 0 p 1

AU - Hochmuth, Reinhard

AU - Garrigós, Gustavo

AU - Tabacco, Anita

N1 - Funding Information: Acknowledgements. Work partially supported by the European Community Human Potential Programme, contracts HPRN-CT-2002-00286 ‘Breaking Complexity’ and HPRN-CT-2001-00273 ‘HARP’. G.G. was also supported by ‘Programa Ramón y Cajal’ and grant BMF2001-0189, MCyT (Spain). The authors thank an anonymous referee whose careful reading and suggestions led to a much improved version of this paper.

PY - 2004/10/1

Y1 - 2004/10/1

N2 - We present a wavelet characterization of anisotropic Besov spaces B p,q α(ℝ n), valid for the whole range 0 < p, q < ∞, and in terms of multi-resolution analyses with dilation adapted to the anisotropy of the space. Our proofs combine classical techniques based on Bernstein and Jackson-type inequalities, and nonlinear methods for the cases p < 1. Among the consequences of our results, we characterize B p,q α as a linear approximation space, and derive embeddings and interpolation formulae for B p,q α, which appear to be new in the literature when p < 1.

AB - We present a wavelet characterization of anisotropic Besov spaces B p,q α(ℝ n), valid for the whole range 0 < p, q < ∞, and in terms of multi-resolution analyses with dilation adapted to the anisotropy of the space. Our proofs combine classical techniques based on Bernstein and Jackson-type inequalities, and nonlinear methods for the cases p < 1. Among the consequences of our results, we characterize B p,q α as a linear approximation space, and derive embeddings and interpolation formulae for B p,q α, which appear to be new in the literature when p < 1.

KW - Mathematics

KW - Approximation and interpolation spaces

KW - Jackson and Bernstein inequalities

KW - Multilevel decomposition

UR - http://www.scopus.com/inward/record.url?scp=8844223347&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/43d575c8-5b17-312a-9b95-457e40847ec8/

U2 - 10.1017/S001309150300107X

DO - 10.1017/S001309150300107X

M3 - Journal articles

VL - 47

SP - 573

EP - 595

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 3

ER -