New classes of weighted Hölder-Zygmund spaces and the wavelet transform (Q442609)

Summary: We provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces \(\mathcal S_0(\mathbb R^n)\) and \(\mathcal S(\mathbb H^{n+1})\). 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.