New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform - Stevan Pilipović; Dušan Rakić; Jasson Vindas (Journal of Function Spaces and Applications)
We provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces 𝒮0(ℝn) and 𝒮(ℍn+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.