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 𝒮0(ℝn) and 𝒮(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 sp...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/815475 |
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| Summary: | We provide a new and elementary proof of the continuity theorem for the wavelet and left-inverse wavelet transforms on the spaces 𝒮0(ℝn) and 𝒮(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. |
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| ISSN: | 0972-6802 1758-4965 |