New Classes of Weighted Hölder-Zygmund Spaces and the Wavelet Transform

الملخص EN

We provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces ?0(ℝn) and ?(ℍn+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.