New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform
New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform
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 H\"older-Zygmund spaces, where the weights are regularly varying functions. The analysis of these …