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

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

2011-12-15

arxiv.org/abs/1112.3678v1

Mathematics

Functional Analysis

17 pages

Scientific paper

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\"{o}lder-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.

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