Wavelet characterizations for anisotropic Besov spaces with 0 p 1

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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.

Original languageEnglish
JournalProceedings of the Edinburgh Mathematical Society
Issue number3
Pages (from-to)573-595
Number of pages23
Publication statusPublished - 01.10.2004
Externally publishedYes

Bibliographical note

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.

    Research areas

  • Mathematics
  • Approximation and interpolation spaces, Jackson and Bernstein inequalities, Multilevel decomposition