Generalised lower Assouad-type dimensions and their interpolations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917256739422208 |
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| author | Chen, Haipeng Wang, Wen |
| author_facet | Chen, Haipeng Wang, Wen |
| contents | This paper investigates the analytic and structural properties of the $ϕ$-lower Assouad dimension, a generalized notion extending the lower Assouad dimension. We establish the equivalence of $ϕ$-lower Assouad dimensions with respect to the dimension functions, prove analytic properties related to the regularity of the $ϕ$-lower dimension, and analyse the role of rate windows in this context. Furthermore, we explore both positive and negative interpolation properties of the $ϕ$-lower dimension by presenting corresponding theorems that delineate these behaviors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07431 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalised lower Assouad-type dimensions and their interpolations Chen, Haipeng Wang, Wen Classical Analysis and ODEs Metric Geometry 28A80 (Primary), 28A78 (Secondary) This paper investigates the analytic and structural properties of the $ϕ$-lower Assouad dimension, a generalized notion extending the lower Assouad dimension. We establish the equivalence of $ϕ$-lower Assouad dimensions with respect to the dimension functions, prove analytic properties related to the regularity of the $ϕ$-lower dimension, and analyse the role of rate windows in this context. Furthermore, we explore both positive and negative interpolation properties of the $ϕ$-lower dimension by presenting corresponding theorems that delineate these behaviors. |
| title | Generalised lower Assouad-type dimensions and their interpolations |
| topic | Classical Analysis and ODEs Metric Geometry 28A80 (Primary), 28A78 (Secondary) |
| url | https://arxiv.org/abs/2602.07431 |