Details
| Original language | English |
|---|---|
| Pages (from-to) | 573-595 |
| Number of pages | 23 |
| Journal | Proceedings of the Edinburgh Mathematical Society |
| Volume | 47 |
| Issue number | 3 |
| Publication status | Published - Oct 2004 |
| Externally published | Yes |
Abstract
We present a wavelet characterization of anisotropic Besov spaces B p,qα(ℝn), 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 Bp,qα as a linear approximation space, and derive embeddings and interpolation formulae for Bp,q α, which appear to be new in the literature when p < 1.
Keywords
- Approximation and interpolation spaces, Jackson and Bernstein inequalities, Multilevel decomposition
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Proceedings of the Edinburgh Mathematical Society, Vol. 47, No. 3, 10.2004, p. 573-595.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Wavelet characterizations for anisotropic Besov spaces with 0 < p < 1
AU - Garrigós, Gustavo
AU - Hochmuth, Reinhard
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
Y1 - 2004/10
N2 - We present a wavelet characterization of anisotropic Besov spaces B p,qα(ℝn), 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 Bp,qα as a linear approximation space, and derive embeddings and interpolation formulae for Bp,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,qα(ℝn), 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 Bp,qα as a linear approximation space, and derive embeddings and interpolation formulae for Bp,q α, which appear to be new in the literature when p < 1.
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
U2 - 10.1017/S001309150300107X
DO - 10.1017/S001309150300107X
M3 - Article
AN - SCOPUS:8844223347
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 -