WAVELET CHARACTERIZATIONS OF MULTI-DIRECTIONAL REGULARITY
The author extends his appreciation to the Deanship of Scientific Research at King Saud University for funding the work through the research group project No. RGP-VPP-024.
MOURAD BEN SLIMANE
Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia
Received: May 5, 2011
Revised: June 20, 2012
Accepted: September 25, 2012
Published: November 19, 2012
The study of d dimensional traces of functions of m several variables leads to directional behaviors. The purpose of this paper is two-fold. Firstly, we extend the notion of one direction pointwise Hölder regularity introduced by Jaffard to multi-directions. Secondly, we characterize multi-directional pointwise regularity by Triebel anisotropic wavelet coefficients (resp. leaders), and also by Calderón anisotropic continuous wavelet transform.
Keywords: Multi-Directional Regularity; Anisotropic Hölder Regularity; Anisotropic Wavelets; Anisotropic Wavelet Transform