Global and local regularity of functions in anisotropic function spaces is analyzed in the common framework provided by hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities derived from the coefficients of hyperbolic wavelet decompositions. A multifractal analysis is introduced, that jointly accounts for scale invariance and anisotropy, and its properties are investigated.
Cite this article
Patrice Abry, Marianne Clausel, Stéphane Jaffard, Stéphane G. Roux, Béatrice Vedel, The hyperbolic wavelet transform: an efficient tool for multifractal analysis of anisotropic fields. Rev. Mat. Iberoam. 31 (2015), no. 1, pp. 313–348DOI 10.4171/RMI/836