New classes of weighted Hölder-Zygmund spaces and the wavelet transform

Abstract

We provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces S 0(ℝ n) and S(ℍ n+1). We then introduce and study a new class of weighted Hölder-Zygmund spaces, where the weights are regularly varying functions. The analysis of these spaces is carried out via the wavelet transform and generalized Littlewood-Paley pairs. Copyright © 2012 Stevan Pilipovi et al.