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arXiv · 1112.3678

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

Stevan Pilipovic·Dusan Rakic·Jasson Vindas
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Abstract

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.

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Stevan Pilipovic, Dusan Rakic, Jasson Vindas. 2018-01-03. New classes of weighted Hölder-Zygmund spaces and the wavelet transform. https://doi.org/10.1155/2012%2F815475

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