Directional and anisotropic regularity and irregularity criteria in Triebel wavelet bases (Q1759436)

The aim of the paper is to study directional and anisotropic regularities of functions. To this end, the authors use anisotropic Hölder-type spaces introduced in \textit{S. Jaffard} [Appl. Comput. Harmon. Anal. 28, No. 3, 251--266 (2010; Zbl 1193.42126)]. In the main results of the paper the authors provide criteria for functions to belong to such spaces. To this purpose, they make use of an anisotropic wavelet transform and decay conditions on Triebel anisotropic wavelet coefficients (resp. wavelet leaders).