Characterization of Hölder and Sobolev spaces via the continuous wavelet transform with rotations

The continuous wavelet transform with rotations in higher dimensions is used to characterize the Hölder and Sobolev spaces for functions f∈L2(Rn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\in L^2({\mathbb {R}}^n)$$\end{document}. Besides we establish the relationship between Hölder continuity and the decay of the continuous wavelet transform with rotations, as well as for the Sobolev spaces.