Wavelet Characterization of Inhomogeneous Lipschitz Spaces on Spaces of Homogeneous Type and Its Applications
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913801158262784 |
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| author | Wang, Fan |
| author_facet | Wang, Fan |
| contents | In this article, the author establishes a wavelet characterization of inhomogeneous Lipschitz space $\mathrm{lip}_θ(\mathcal{X})$ via Carlson sequence, where $\mathcal{X}$ is a space of homogeneous type introduced by R. R. Coifman and G. Weiss. As applications, characterizations of several geometric conditions on $\mathcal{X}$, involving the upper bound, the lower bound, and the Ahlfors regular condition, are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wavelet Characterization of Inhomogeneous Lipschitz Spaces on Spaces of Homogeneous Type and Its Applications Wang, Fan Classical Analysis and ODEs Analysis of PDEs In this article, the author establishes a wavelet characterization of inhomogeneous Lipschitz space $\mathrm{lip}_θ(\mathcal{X})$ via Carlson sequence, where $\mathcal{X}$ is a space of homogeneous type introduced by R. R. Coifman and G. Weiss. As applications, characterizations of several geometric conditions on $\mathcal{X}$, involving the upper bound, the lower bound, and the Ahlfors regular condition, are obtained. |
| title | Wavelet Characterization of Inhomogeneous Lipschitz Spaces on Spaces of Homogeneous Type and Its Applications |
| topic | Classical Analysis and ODEs Analysis of PDEs |
| url | https://arxiv.org/abs/2504.14816 |