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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2408.05227 |
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| _version_ | 1866916811874762752 |
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| author | Sun, Chuhan Wang, Zhiming |
| author_facet | Sun, Chuhan Wang, Zhiming |
| contents | We establish Triebel-Lizorkin spaces in the Dunkl setting which are associated with finite reflection groups on the Euclidean space. The group structures induce two nonequivalent metrics: the Euclidean metric and the Dunkl metric. In this paper, the L^2 space and the Dunkl-Calderon-Zygmund singular integral operator in the Dunkl setting play a fundamental role. The main tools used in this paper are as follows: (i) the Dunkl-Calderon-Zygmund singular integral operator and a new Calderon reproducing formula in L^2 with the Triebel-Lizorkin space norms; (ii) new test functions in terms of the L^2 functions and distributions; (iii) the Triebel-Lizorkin spaces in the Dunkl setting which are defined by the wavelet-type decomposition with norms and the analogous atomic decomposition of the Hardy spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triebel-Lizorkin spaces in Dunkl setting Sun, Chuhan Wang, Zhiming Classical Analysis and ODEs We establish Triebel-Lizorkin spaces in the Dunkl setting which are associated with finite reflection groups on the Euclidean space. The group structures induce two nonequivalent metrics: the Euclidean metric and the Dunkl metric. In this paper, the L^2 space and the Dunkl-Calderon-Zygmund singular integral operator in the Dunkl setting play a fundamental role. The main tools used in this paper are as follows: (i) the Dunkl-Calderon-Zygmund singular integral operator and a new Calderon reproducing formula in L^2 with the Triebel-Lizorkin space norms; (ii) new test functions in terms of the L^2 functions and distributions; (iii) the Triebel-Lizorkin spaces in the Dunkl setting which are defined by the wavelet-type decomposition with norms and the analogous atomic decomposition of the Hardy spaces. |
| title | Triebel-Lizorkin spaces in Dunkl setting |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2408.05227 |