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New classes of weighted H\"older-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 S0(Rn) \mathcal{S}_0(\mathbb{R}^n) and S(Hn+1) \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 spaces is carried out via the wavelet transform and generalized Littlewood-Paley pairs.Comment: 18 page

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