Journal of Fourier Analysis and Applications

, Volume 18, Issue 5, pp 893–914 | Cite as

Directional and Anisotropic Regularity and Irregularity Criteria in Triebel Wavelet Bases

Article
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Revised:

Abstract

Many natural mathematical objects, as well as many multi-dimensional signals and images from real physical problems, need to distinguish local directional behaviors (for tracking contours in image processing for example). Using some results of Jaffard and Triebel, we obtain criteria of directional and anisotropic regularities by decay conditions on Triebel anisotropic wavelet coefficients (resp. wavelet leaders).

Keywords

Directional regularity Anisotropic Hölder regularity Anisotropic Triebel wavelet basis Anisotropic wavelet coefficients Anisotropic wavelet leaders 

Mathematics Subject Classification

26A16 26B35 42C40 

Notes

Acknowledgements

Mourad Ben Slimane is thankful to Stéphane Jaffard for stimulating discussions. The authors are very grateful to the referees for their comments and remarks that greatly helped improve the presentation of the paper.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceKing Saud UniversityRiyadhSaudi Arabia
  2. 2.Institut de Mathématiques de JussieuParisFrance
  3. 3.Université Tunis El ManarTunisTunisia

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